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Math Problems
Algebra 1
Multiplication with rational exponents
Which expressions are equivalent to
1
5
⋅
1
5
⋅
1
5
⋅
1
5
?
\frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} ?
5
1
⋅
5
1
⋅
5
1
⋅
5
1
?
\newline
Choose
2
2
2
answers:
\newline
(A)
(
5
−
2
)
2
\left(5^{-2}\right)^{2}
(
5
−
2
)
2
\newline
(B)
(
5
−
4
)
0
\left(5^{-4}\right)^{0}
(
5
−
4
)
0
\newline
(C)
5
1
5
4
\frac{5^{1}}{5^{4}}
5
4
5
1
\newline
(D)
5
2
⋅
5
−
6
5^{2} \cdot 5^{-6}
5
2
⋅
5
−
6
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For
j
(
x
)
=
(
−
2
x
2
−
1
)
(
−
3
x
3
+
2
x
)
j(x)=\left(-2 x^{2}-1\right)\left(-3 x^{3}+2 x\right)
j
(
x
)
=
(
−
2
x
2
−
1
)
(
−
3
x
3
+
2
x
)
, find
j
′
(
1
)
j^{\prime}(1)
j
′
(
1
)
by applying the product rule.
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The expression
x
3
+
2
x
2
+
x
+
6
x
+
2
\frac{x^{3}+2 x^{2}+x+6}{x+2}
x
+
2
x
3
+
2
x
2
+
x
+
6
is equivalent to
\newline
(
1
1
1
)
x
2
+
3
x^{2}+3
x
2
+
3
\newline
(
3
3
3
)
2
x
2
+
x
+
6
2 x^{2}+x+6
2
x
2
+
x
+
6
\newline
(
2
2
2
)
x
2
+
1
+
4
x
+
2
x^{2}+1+\frac{4}{x+2}
x
2
+
1
+
x
+
2
4
\newline
(
4
4
4
)
2
x
2
+
1
+
4
x
+
2
2 x^{2}+1+\frac{4}{x+2}
2
x
2
+
1
+
x
+
2
4
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8
⋅
5
−
t
9
=
346
8 \cdot 5^{\frac{-t}{9}}=346
8
⋅
5
9
−
t
=
346
\newline
Which of the following is the solution of the equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
t
=
9
log
5
(
43.25
)
t=9 \log _{5}(43.25)
t
=
9
lo
g
5
(
43.25
)
\newline
(B)
t
=
−
9
log
40
(
346
)
t=-9 \log _{40}(346)
t
=
−
9
lo
g
40
(
346
)
\newline
(C)
t
=
−
9
log
5
(
43.25
)
t=-9 \log _{5}(43.25)
t
=
−
9
lo
g
5
(
43.25
)
\newline
(D)
t
=
9
log
346
(
40
)
t=9 \log _{346}(40)
t
=
9
lo
g
346
(
40
)
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Write the expression as a single logarithm.
\newline
7
log
c
x
−
1
4
log
c
w
+
2
log
c
z
7 \log _{c} x-\frac{1}{4} \log _{c} w+2 \log _{c} z
7
lo
g
c
x
−
4
1
lo
g
c
w
+
2
lo
g
c
z
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Mary spent
2
5
\frac{2}{5}
5
2
hour waiting for the school bus and
3
10
\frac{3}{10}
10
3
hour riding the bus to school. How much time did Mary spend in all?
\newline
Give your answer in simplest form.
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Which fraction has the same value as
6
−
2
⋅
2
4
1
2
6^{-2} \cdot 24^{\frac{1}{2}}
6
−
2
⋅
2
4
2
1
?
\newline
(A)
1
144
\frac{1}{144}
144
1
\newline
(B)
2
6
\frac{\sqrt{2}}{6}
6
2
\newline
(C)
6
18
\frac{\sqrt{6}}{18}
18
6
\newline
(D)
1
3
\frac{1}{3}
3
1
Get tutor help
Select the equivalent expression.
\newline
(
2
−
10
4
2
)
7
=
?
\left(\frac{2^{-10}}{4^{2}}\right)^{7}=?
(
4
2
2
−
10
)
7
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
2
70
⋅
4
14
\frac{1}{2^{70} \cdot 4^{14}}
2
70
⋅
4
14
1
\newline
(B)
2
84
2^{84}
2
84
\newline
(C)
2
−
3
⋅
4
−
9
2^{-3} \cdot 4^{-9}
2
−
3
⋅
4
−
9
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83
83
83
. Prove the identity.
\newline
2
(
tan
x
−
cot
x
)
tan
2
x
−
cot
2
x
=
sin
2
x
\frac{2(\tan x-\cot x)}{\tan ^{2} x-\cot ^{2} x}=\sin 2 x
tan
2
x
−
cot
2
x
2
(
tan
x
−
cot
x
)
=
sin
2
x
Get tutor help
Select the equivalent expression.
\newline
(
5
4
⋅
b
−
10
)
−
6
=
?
\left(5^{4} \cdot b^{-10}\right)^{-6}=?
(
5
4
⋅
b
−
10
)
−
6
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
b
60
5
24
\frac{b^{60}}{5^{24}}
5
24
b
60
\newline
(B)
5
4
⋅
b
60
5^{4} \cdot b^{60}
5
4
⋅
b
60
\newline
(C)
5
24
⋅
b
60
5^{24} \cdot b^{60}
5
24
⋅
b
60
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Simplify.
\newline
Rewrite the expression in the form
6
n
6^{n}
6
n
.
\newline
6
−
6
6
−
5
=
\frac{6^{-6}}{6^{-5}}=
6
−
5
6
−
6
=
Get tutor help
(
3
−
6
7
−
3
)
5
=
?
\left(\frac{3^{-6}}{7^{-3}}\right)^{5}=?
(
7
−
3
3
−
6
)
5
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
7
15
3
30
\frac{7^{15}}{3^{30}}
3
30
7
15
\newline
(B)
3
15
7
30
\frac{3^{15}}{7^{30}}
7
30
3
15
\newline
(C)
7
3
3
−
30
\frac{7^{3}}{3^{-30}}
3
−
30
7
3
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Which expressions are equivalent to
7
−
2
⋅
7
6
7^{-2} \cdot 7^{6}
7
−
2
⋅
7
6
?
\newline
Choose
1
1
1
answer:
\newline
(A)
7
2
7
−
2
\frac{7^{2}}{7^{-2}}
7
−
2
7
2
\newline
(B)
7
6
7
−
2
\frac{7^{6}}{7^{-2}}
7
−
2
7
6
\newline
(C)
7
−
12
7^{-12}
7
−
12
\newline
(D)
(
7
2
)
2
(7^{2})^{2}
(
7
2
)
2
Get tutor help
y
(
1
2
)
16
x
2
y
(
3
2
)
+
8
y
2
3
y^{\left(\frac{1}{2}\right)}\sqrt[3]{16x^{2}y^{\left(\frac{3}{2}\right)}+8y^{2}}
y
(
2
1
)
3
16
x
2
y
(
2
3
)
+
8
y
2
\newline
Which of the following expressions is equivalent to the given expression assuming
y
≥
0
y \geq 0
y
≥
0
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
y
2
x
2
+
y
(
1
2
)
3
2y\sqrt[3]{2x^{2}+y^{\left(\frac{1}{2}\right)}}
2
y
3
2
x
2
+
y
(
2
1
)
\newline
(B)
24
x
2
y
(
7
2
)
3
∗
y
(
1
2
)
\sqrt[3]{24x^{2}y^{\left(\frac{7}{2}\right)}}*y^{\left(\frac{1}{2}\right)}
3
24
x
2
y
(
2
7
)
∗
y
(
2
1
)
\newline
(C)
y
16
x
2
3
+
2
y
(
7
6
)
y\sqrt[3]{16x^{2}}+2y^{\left(\frac{7}{6}\right)}
y
3
16
x
2
+
2
y
(
6
7
)
\newline
(D)
16
x
2
y
2
+
8
y
(
5
2
)
3
\sqrt[3]{16x^{2}y^{2}+8y^{\left(\frac{5}{2}\right)}}
3
16
x
2
y
2
+
8
y
(
2
5
)
Get tutor help
Solve:
(
a
−
7
b
−
2
)
−
9
=
?
(a^{-7}b^{-2})^{-9}=?
(
a
−
7
b
−
2
)
−
9
=
?
Get tutor help
Simplify.
(
3
6
y
−
5
)
2
=
?
\left(\frac{3^6}{y^{-5}}\right)^2=?
(
y
−
5
3
6
)
2
=
?
Get tutor help
Which expressions are equivalent to
(
b
2
)
1
9
(b^{2})^{\frac{1}{9}}
(
b
2
)
9
1
?
\newline
Choose all answers that apply:
\newline
(
A
)
(A)
(
A
)
(
b
−
1
9
)
2
(b^{-\frac{1}{9}})^{2}
(
b
−
9
1
)
2
\newline
(
B
)
(B)
(
B
)
(
b
1
9
)
2
(b^{\frac{1}{9}})^{2}
(
b
9
1
)
2
\newline
(
C
)
(C)
(
C
)
(
b
1
2
)
9
(b^{\frac{1}{2}})^{9}
(
b
2
1
)
9
\newline
(
D
)
(D)
(
D
)
None of the above
Get tutor help
Which of the following numbers are greater than
−
0.33
-0.33
−
0.33
?
\newline
Choose all answers that apply:
\newline
(
A
)
(A)
(
A
)
−
0.3
-0.3
−
0.3
\newline
(
B
)
(B)
(
B
)
−
3
9
-\frac{3}{9}
−
9
3
\newline
(
C
)
(C)
(
C
)
1
6
\frac{1}{6}
6
1
Get tutor help
Subtract the polynomials as indicated.
\newline
(
7
m
3
+
9
m
2
−
m
+
2.2
)
−
(
−
3
m
3
+
3
m
+
3.6
)
(7m^{3}+9m^{2}-m+2.2)-(-3m^{3}+3m+3.6)
(
7
m
3
+
9
m
2
−
m
+
2.2
)
−
(
−
3
m
3
+
3
m
+
3.6
)
Get tutor help
Evaluate
∑
m
=
1
(
2
m
)
!
m
2
m
\sum_{m=1} \frac{(2m)!}{m^{2m}}
∑
m
=
1
m
2
m
(
2
m
)!
Get tutor help
(
4
5
)
⋅
(
4
7
)
(\frac{4}{5})\cdot(\frac{4}{7})
(
5
4
)
⋅
(
7
4
)
\newline
Enter the numerator.
Get tutor help
6
6
6
erasers cost
$
6.60
\$6.60
$6.60
.
\newline
Which equation would help determine the cost of
3
3
3
erasers?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
x
=
$
6.60
6
\frac{3}{x} = \frac{\$6.60}{6}
x
3
=
6
$6.60
\newline
(B)
3
6
=
$
6.60
x
\frac{3}{6} = \frac{\$6.60}{x}
6
3
=
x
$6.60
\newline
(C)
x
3
=
6
$
6.60
\frac{x}{3} = \frac{6}{\$6.60}
3
x
=
$6.60
6
\newline
(D)
x
3
=
$
6.60
6
\frac{x}{3} = \frac{\$6.60}{6}
3
x
=
6
$6.60
\newline
(E) None of the above
Get tutor help
Solve:
\newline
1
4
+
(
−
7
9
)
=
\quad \frac{1}{4} + \left(-\frac{7}{9}\right) =
4
1
+
(
−
9
7
)
=
Get tutor help
Solve the expression:
\newline
(
13
1
12
+
4
11
12
)
−
6
9
40
(13\frac{1}{12}+4\frac{11}{12})-6\frac{9}{40}
(
13
12
1
+
4
12
11
)
−
6
40
9
Get tutor help
Simplify
(
3
25
)
\sqrt{\left(\frac{3}{25}\right)}
(
25
3
)
.
\newline
(A)
3
5
\frac{3}{5}
5
3
\newline
(B)
3
5
\frac{\sqrt{3}}{5}
5
3
\newline
(C)
3
25
\frac{\sqrt{3}}{25}
25
3
\newline
(D)
3
25
\frac{3}{25}
25
3
Get tutor help
Divide:
\newline
3
4
÷
3
7
=
\frac{3}{4}\div\frac{3}{7}=
4
3
÷
7
3
=
Get tutor help
Select the answer which is equivalent to the given expression using your calculator.
\newline
sin
(
arcsin
11
14
)
\sin \left(\arcsin \frac{11}{14}\right)
sin
(
arcsin
14
11
)
\newline
75
14
\frac{\sqrt{75}}{14}
14
75
\newline
11
14
\frac{11}{14}
14
11
\newline
14
11
\frac{14}{11}
11
14
\newline
75
11
\frac{\sqrt{75}}{11}
11
75
Get tutor help
Select the answer which is equivalent to the given expression using your calculator.
\newline
17
−
4
−
18
\frac{17}{-4-\sqrt{18}}
−
4
−
18
17
\newline
136
+
34
18
2
\frac{136+34 \sqrt{18}}{2}
2
136
+
34
18
\newline
68
−
17
18
2
\frac{68-17 \sqrt{18}}{2}
2
68
−
17
18
\newline
68
+
17
18
2
\frac{68+17 \sqrt{18}}{2}
2
68
+
17
18
\newline
136
−
34
18
2
\frac{136-34 \sqrt{18}}{2}
2
136
−
34
18
Get tutor help
Select the answer which is equivalent to the given expression using your calculator.
\newline
15
−
20
−
10
\frac{15}{-20-\sqrt{10}}
−
20
−
10
15
\newline
−
20
+
10
13
\frac{-20+\sqrt{10}}{13}
13
−
20
+
10
\newline
−
20
−
10
13
\frac{-20-\sqrt{10}}{13}
13
−
20
−
10
\newline
−
20
−
10
26
\frac{-20-\sqrt{10}}{26}
26
−
20
−
10
\newline
−
20
+
10
26
\frac{-20+\sqrt{10}}{26}
26
−
20
+
10
Get tutor help
Select the answer which is equivalent to the given expression using your calculator.
\newline
−
4
a
2
(
3125
b
)
2
5
a
=
4
and
b
=
243
\begin{array}{c} \frac{-4 a^{2}}{(3125 b)^{\frac{2}{5}}} \\ a=4 \text { and } b=243 \end{array}
(
3125
b
)
5
2
−
4
a
2
a
=
4
and
b
=
243
\newline
−
64
225
-\frac{64}{225}
−
225
64
\newline
64
225
\frac{64}{225}
225
64
\newline
8
225
\frac{8}{225}
225
8
\newline
−
8
225
-\frac{8}{225}
−
225
8
Get tutor help
Select the answer which is equivalent to the given expression using your calculator.
\newline
a
=
4
and
b
=
243
a=4 \text { and } b=243
a
=
4
and
b
=
243
\newline
−
64
225
-\frac{64}{225}
−
225
64
\newline
64
225
\frac{64}{225}
225
64
\newline
8
225
\frac{8}{225}
225
8
\newline
−
8
225
-\frac{8}{225}
−
225
8
Get tutor help
Select the answer which is equivalent to the given expression using your calculator.
\newline
8
a
3
2
−
4
b
3
\frac{8 a^{\frac{3}{2}}}{-4 b^{3}}
−
4
b
3
8
a
2
3
\newline
a
=
9
and
b
=
−
4
a=9 \text { and } b=-4
a
=
9
and
b
=
−
4
\newline
−
27
32
-\frac{27}{32}
−
32
27
\newline
27
32
\frac{27}{32}
32
27
\newline
−
27
512
-\frac{27}{512}
−
512
27
\newline
27
512
\frac{27}{512}
512
27
Get tutor help
Select the answer which is equivalent to the given expression using your calculator.
\newline
6
a
−
2
5
b
−
2
3
a
=
−
3
and
b
=
64
\begin{array}{c} \frac{6 a^{-2}}{5 b^{-\frac{2}{3}}} \\ a=-3 \text { and } b=64 \end{array}
5
b
−
3
2
6
a
−
2
a
=
−
3
and
b
=
64
\newline
−
32
15
-\frac{32}{15}
−
15
32
\newline
32
15
\frac{32}{15}
15
32
\newline
32
45
\frac{32}{45}
45
32
\newline
−
32
45
-\frac{32}{45}
−
45
32
Get tutor help
Select the answer which is equivalent to the given expression using your calculator.
\newline
(
−
6
a
)
2
(
5
b
)
4
\frac{(-6 a)^{2}}{(5 b)^{4}}
(
5
b
)
4
(
−
6
a
)
2
\newline
a
=
−
5
and
b
=
−
6
a=-5 \text { and } b=-6
a
=
−
5
and
b
=
−
6
\newline
1
900
\frac{1}{900}
900
1
\newline
1
1800
\frac{1}{1800}
1800
1
\newline
−
1
900
-\frac{1}{900}
−
900
1
\newline
−
1
1800
-\frac{1}{1800}
−
1800
1
Get tutor help
Select the answer which is equivalent to the given expression using your calculator.
\newline
13
−
20
+
15
\frac{13}{-20+\sqrt{15}}
−
20
+
15
13
\newline
−
260
+
13
15
385
\frac{-260+13 \sqrt{15}}{385}
385
−
260
+
13
15
\newline
−
20
−
15
385
\frac{-20-\sqrt{15}}{385}
385
−
20
−
15
\newline
−
260
−
13
15
385
\frac{-260-13 \sqrt{15}}{385}
385
−
260
−
13
15
\newline
−
20
+
15
385
\frac{-20+\sqrt{15}}{385}
385
−
20
+
15
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Select the answer which is equivalent to the given expression using your calculator.
\newline
−
5
−
20
+
5
\frac{-5}{-20+\sqrt{5}}
−
20
+
5
−
5
\newline
20
−
5
79
\frac{20-\sqrt{5}}{79}
79
20
−
5
\newline
20
+
5
79
\frac{20+\sqrt{5}}{79}
79
20
+
5
\newline
60
+
3
5
79
\frac{60+3 \sqrt{5}}{79}
79
60
+
3
5
\newline
60
−
3
5
79
\frac{60-3 \sqrt{5}}{79}
79
60
−
3
5
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Select the answer which is equivalent to the given expression using your calculator.
\newline
log
729
243
\log _{729} 243
lo
g
729
243
\newline
7
6
\frac{7}{6}
6
7
\newline
6
7
\frac{6}{7}
7
6
\newline
5
6
\frac{5}{6}
6
5
\newline
6
5
\frac{6}{5}
5
6
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Select the answer which is equivalent to the given expression using your calculator.
\newline
log
343
49
\log _{343} 49
lo
g
343
49
\newline
2
3
\frac{2}{3}
3
2
\newline
2
5
\frac{2}{5}
5
2
\newline
5
2
\frac{5}{2}
2
5
\newline
3
2
\frac{3}{2}
2
3
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Select the answer which is equivalent to the given expression using your calculator.
\newline
tan
A
=
13
84
and
cos
B
=
72
75
\tan A=\frac{13}{84} \text { and } \cos B=\frac{72}{75}
tan
A
=
84
13
and
cos
B
=
75
72
\newline
Angles A and B are in Quadrant I.
\newline
Find
sin
(
A
+
B
)
\sin (A+B)
sin
(
A
+
B
)
.
\newline
−
828
6375
\frac{-828}{6375}
6375
−
828
\newline
2700
6375
\frac{2700}{6375}
6375
2700
\newline
5775
6375
\frac{5775}{6375}
6375
5775
\newline
6321
6375
\frac{6321}{6375}
6375
6321
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(
y
x
+
x
y
=
−
2
)
d
d
x
\left(\frac{y}{x}+xy=-2\right)\frac{d}{dx}
(
x
y
+
x
y
=
−
2
)
d
x
d
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What is the product of
(
2
10
)
⋅
(
4
5
)
⋅
(
3
2
)
(\frac{2}{10})\cdot(\frac{4}{5})\cdot(\frac{3}{2})
(
10
2
)
⋅
(
5
4
)
⋅
(
2
3
)
? Express your answer in the simplest fraction.
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[
(
9
f
+
9
)
+
(
9
f
+
9
+
1
)
]
⋅
f
[(9f+9)+(9f+9+1)]\cdot f
[(
9
f
+
9
)
+
(
9
f
+
9
+
1
)]
⋅
f
which of the following expressions is eqivilant to the expression given
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Last year, the total revenue for Home Style, a national restaurant chain, increased
5.25
%
5.25 \%
5.25%
over the previous year. If this trend were to continue, which expression could the company's chief financial officer use to approximate their monthly percent increase in revenue? [Let
m
m
m
represent months.]
\newline
(
1
1
1
)
(
1.0525
)
m
t
(1.0525)^{m t}
(
1.0525
)
m
t
\newline
(
3
3
3
)
(
1.00427
)
m
(1.00427)^{m}
(
1.00427
)
m
\newline
(
2
2
2
)
(
1.0525
)
12
m
(1.0525)^{\frac{12}{m}}
(
1.0525
)
m
12
\newline
(
4
4
4
)
(
1.00427
)
m
12
(1.00427)^{\frac{m}{12}}
(
1.00427
)
12
m
Get tutor help
Evaluate.
\newline
log
4
4
4
\log _{4} \sqrt[4]{4}
lo
g
4
4
4
\newline
Write your answer in simplest form.
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Find the sum of the first
9
9
9
terms of the following series, to the nearest integer.
\newline
2
,
5
2
,
25
8
,
…
2, \frac{5}{2}, \frac{25}{8}, \ldots
2
,
2
5
,
8
25
,
…
\newline
Answer:
Get tutor help
Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
(
8
−
1
3
log
8
27
w
3
)
\left(8^{-\frac{1}{3} \log _{8} 27 w^{3}}\right)
(
8
−
3
1
l
o
g
8
27
w
3
)
\newline
Answer:
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Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
(
3
−
3
log
3
4
x
2
)
\left(3^{-3 \log _{3} 4 x^{2}}\right)
(
3
−
3
l
o
g
3
4
x
2
)
\newline
Answer:
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Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
(
2
log
2
(
4
w
x
)
)
\left(2^{\log _{2}(4 w x)}\right)
(
2
l
o
g
2
(
4
w
x
)
)
\newline
Answer:
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Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
(
8
log
8
(
6
w
3
)
+
log
8
(
2
z
3
)
)
\left(8^{\log _{8}\left(6 w^{3}\right)+\log _{8}\left(2 z^{3}\right)}\right)
(
8
l
o
g
8
(
6
w
3
)
+
l
o
g
8
(
2
z
3
)
)
\newline
Answer:
Get tutor help
Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
(
3
log
3
(
4
x
3
)
−
log
3
(
7
w
)
)
\left(3^{\log _{3}\left(4 x^{3}\right)-\log _{3}(7 w)}\right)
(
3
l
o
g
3
(
4
x
3
)
−
l
o
g
3
(
7
w
)
)
\newline
Answer:
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