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Math Problems
Algebra 1
Multiplication with rational exponents
Which expression is equivalent to
2
8
⋅
2
5
2
5
?
2^{8} \cdot \frac{2^{5}}{2^{5}} ?
2
8
⋅
2
5
2
5
?
\newline
2
9
2^{9}
2
9
\newline
2
8
2^{8}
2
8
\newline
2
7
2^{7}
2
7
\newline
1
1
1
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Which expression is equivalent to
(
4
−
4
)
−
5
4
5
?
\frac{\left(4^{-4}\right)^{-5}}{4^{5}} ?
4
5
(
4
−
4
)
−
5
?
\newline
4
−
14
4^{-14}
4
−
14
\newline
4
15
4^{15}
4
15
\newline
4
−
25
4^{-25}
4
−
25
\newline
4
17
4^{17}
4
17
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Which expression is equivalent to
3
−
6
⋅
3
−
6
3
−
1
?
3^{-6} \cdot \frac{3^{-6}}{3^{-1}} ?
3
−
6
⋅
3
−
1
3
−
6
?
\newline
3
30
3^{30}
3
30
\newline
3
−
10
3^{-10}
3
−
10
\newline
3
−
11
3^{-11}
3
−
11
\newline
3
−
1
3^{-1}
3
−
1
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Which expression is equivalent to
(
4
3
)
0
4
−
3
?
\frac{\left(4^{3}\right)^{0}}{4^{-3}} ?
4
−
3
(
4
3
)
0
?
\newline
0
0
0
\newline
4
−
3
4^{-3}
4
−
3
\newline
1
1
1
\newline
4
3
4^{3}
4
3
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Which expression is equivalent to
4
3
4
−
7
⋅
4
7
?
\frac{4^{3}}{4^{-7} \cdot 4^{7}} ?
4
−
7
⋅
4
7
4
3
?
\newline
16
16
16
\newline
1
64
\frac{1}{64}
64
1
\newline
64
64
64
\newline
4
4
4
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Which expression is equivalent to
(
4
−
2
⋅
4
6
)
−
5
?
\left(4^{-2} \cdot 4^{6}\right)^{-5} ?
(
4
−
2
⋅
4
6
)
−
5
?
\newline
4
−
20
4^{-20}
4
−
20
\newline
4
−
17
4^{-17}
4
−
17
\newline
4
−
16
4^{-16}
4
−
16
\newline
4
60
4^{60}
4
60
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Which expression is equivalent to
6
−
2
(
6
0
)
−
1
?
\frac{6^{-2}}{\left(6^{0}\right)^{-1}} ?
(
6
0
)
−
1
6
−
2
?
\newline
1
36
\frac{1}{36}
36
1
\newline
36
36
36
\newline
0
0
0
\newline
1
1
1
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
−
2
3
6
\frac{-\frac{2}{3}}{6}
6
−
3
2
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
−
4
7
−
5
8
\frac{-\frac{4}{7}}{-\frac{5}{8}}
−
8
5
−
7
4
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
−
1
3
⋅
−
2
3
-\frac{1}{3} \cdot-\frac{2}{3}
−
3
1
⋅
−
3
2
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
−
3
4
−
5
\frac{-\frac{3}{4}}{-5}
−
5
−
4
3
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
−
1
2
⋅
1
3
-\frac{1}{2} \cdot \frac{1}{3}
−
2
1
⋅
3
1
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
3
4
÷
−
9
7
\frac{3}{4} \div-\frac{9}{7}
4
3
÷
−
7
9
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
−
4
9
⋅
5
2
-\frac{4}{9} \cdot \frac{5}{2}
−
9
4
⋅
2
5
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
1
2
⋅
−
10
9
\frac{1}{2} \cdot-\frac{10}{9}
2
1
⋅
−
9
10
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
1
4
⋅
−
1
4
\frac{1}{4} \cdot-\frac{1}{4}
4
1
⋅
−
4
1
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
3
2
−
5
6
\frac{\frac{3}{2}}{-\frac{5}{6}}
−
6
5
2
3
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
7
8
⋅
−
2
3
\frac{7}{8} \cdot-\frac{2}{3}
8
7
⋅
−
3
2
\newline
Answer:
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
−
1
6
⋅
−
4
5
-\frac{1}{6} \cdot-\frac{4}{5}
−
6
1
⋅
−
5
4
\newline
Answer:
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Fully simplify to one fraction.
\newline
7
x
+
6
−
x
x
2
−
x
−
42
\frac{7}{x+6}-\frac{x}{x^{2}-x-42}
x
+
6
7
−
x
2
−
x
−
42
x
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If
1
5
h
+
25
=
d
\frac{1}{5}h+25=d
5
1
h
+
25
=
d
, which of the following expressions is equivalent to
h
h
h
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
5
d
−
5
\frac{1}{5}d-5
5
1
d
−
5
\newline
(B)
1
5
d
+
25
\frac{1}{5}d+25
5
1
d
+
25
\newline
(C)
5
d
−
125
5d-125
5
d
−
125
\newline
(D)
5
d
−
25
5d-25
5
d
−
25
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Select the equivalent expression.
\newline
(
3
3
⋅
6
6
)
−
3
=
(3^{3}\cdot6^{6})^{-3}=
(
3
3
⋅
6
6
)
−
3
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
3
9
⋅
6
18
\frac{1}{3^{9}\cdot6^{18}}
3
9
⋅
6
18
1
\newline
(B)
6
18
3
9
\frac{6^{18}}{3^{9}}
3
9
6
18
\newline
(C)
3
9
6
18
\frac{3^{9}}{6^{18}}
6
18
3
9
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Solve for
y
y
y
. Express your answer as a proper or improper fraction in simplest terms.
\newline
−
1
2
=
−
1
4
−
4
7
y
-\frac{1}{2}=-\frac{1}{4}-\frac{4}{7} y
−
2
1
=
−
4
1
−
7
4
y
\newline
Answer:
y
=
y=
y
=
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Which expression has the same value as
−
10
x
+
7
y
-10 x+7 y
−
10
x
+
7
y
?
\newline
−
7
y
−
(
−
10
x
)
-7 y-(-10 x)
−
7
y
−
(
−
10
x
)
\newline
−
10
x
−
7
y
-10 x-7 y
−
10
x
−
7
y
\newline
−
10
x
−
(
−
7
y
)
-10 x-(-7 y)
−
10
x
−
(
−
7
y
)
\newline
7
y
−
(
−
10
x
)
7 y-(-10 x)
7
y
−
(
−
10
x
)
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Which expression has the same value as
62.7
+
(
−
85.6
)
62.7+(-85.6)
62.7
+
(
−
85.6
)
?
\newline
−
62.7
−
(
−
85.6
)
-62.7-(-85.6)
−
62.7
−
(
−
85.6
)
\newline
85.6
+
62.7
85.6+62.7
85.6
+
62.7
\newline
−
85.6
−
(
−
62.7
)
-85.6-(-62.7)
−
85.6
−
(
−
62.7
)
\newline
−
85.6
−
62.7
-85.6-62.7
−
85.6
−
62.7
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Which expression is equivalent to
−
9
2
3
+
8
1
6
-9 \frac{2}{3}+8 \frac{1}{6}
−
9
3
2
+
8
6
1
?
\newline
8
1
6
+
9
2
3
8 \frac{1}{6}+9 \frac{2}{3}
8
6
1
+
9
3
2
\newline
−
9
2
3
−
(
−
8
1
6
)
-9 \frac{2}{3}-\left(-8 \frac{1}{6}\right)
−
9
3
2
−
(
−
8
6
1
)
\newline
−
9
2
3
−
8
1
6
-9 \frac{2}{3}-8 \frac{1}{6}
−
9
3
2
−
8
6
1
\newline
8
1
6
−
(
−
9
2
3
)
8 \frac{1}{6}-\left(-9 \frac{2}{3}\right)
8
6
1
−
(
−
9
3
2
)
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Which expression is equivalent to
−
10
1
5
+
(
−
6
3
5
)
-10 \frac{1}{5}+\left(-6 \frac{3}{5}\right)
−
10
5
1
+
(
−
6
5
3
)
?
\newline
10
1
5
−
(
−
6
3
5
)
10 \frac{1}{5}-\left(-6 \frac{3}{5}\right)
10
5
1
−
(
−
6
5
3
)
\newline
−
6
3
5
−
10
1
5
-6 \frac{3}{5}-10 \frac{1}{5}
−
6
5
3
−
10
5
1
\newline
−
10
1
5
+
6
3
5
-10 \frac{1}{5}+6 \frac{3}{5}
−
10
5
1
+
6
5
3
\newline
6
3
5
+
(
−
10
1
5
)
6 \frac{3}{5}+\left(-10 \frac{1}{5}\right)
6
5
3
+
(
−
10
5
1
)
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Which expression has the same value as
−
4
3
4
+
3
1
6
-4 \frac{3}{4}+3 \frac{1}{6}
−
4
4
3
+
3
6
1
?
\newline
4
3
4
−
3
1
6
4 \frac{3}{4}-3 \frac{1}{6}
4
4
3
−
3
6
1
\newline
−
4
3
4
−
3
1
6
-4 \frac{3}{4}-3 \frac{1}{6}
−
4
4
3
−
3
6
1
\newline
3
1
6
−
4
3
4
3 \frac{1}{6}-4 \frac{3}{4}
3
6
1
−
4
4
3
\newline
−
3
1
6
+
(
−
4
3
4
)
-3 \frac{1}{6}+\left(-4 \frac{3}{4}\right)
−
3
6
1
+
(
−
4
4
3
)
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Which expression has the same value as
2
5
6
−
3
3
5
2 \frac{5}{6}-3 \frac{3}{5}
2
6
5
−
3
5
3
?
\newline
−
3
3
5
−
2
5
6
-3 \frac{3}{5}-2 \frac{5}{6}
−
3
5
3
−
2
6
5
\newline
2
5
6
−
(
−
3
3
5
)
2 \frac{5}{6}-\left(-3 \frac{3}{5}\right)
2
6
5
−
(
−
3
5
3
)
\newline
−
3
3
5
+
(
−
2
5
6
)
-3 \frac{3}{5}+\left(-2 \frac{5}{6}\right)
−
3
5
3
+
(
−
2
6
5
)
\newline
−
3
3
5
+
2
5
6
-3 \frac{3}{5}+2 \frac{5}{6}
−
3
5
3
+
2
6
5
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Which expression has the same value as
1
3
4
+
8
2
5
1 \frac{3}{4}+8 \frac{2}{5}
1
4
3
+
8
5
2
?
\newline
−
1
3
4
+
8
2
5
-1 \frac{3}{4}+8 \frac{2}{5}
−
1
4
3
+
8
5
2
\newline
−
8
2
5
−
1
3
4
-8 \frac{2}{5}-1 \frac{3}{4}
−
8
5
2
−
1
4
3
\newline
1
3
4
−
(
−
8
2
5
)
1 \frac{3}{4}-\left(-8 \frac{2}{5}\right)
1
4
3
−
(
−
8
5
2
)
\newline
1
3
4
−
8
2
5
1 \frac{3}{4}-8 \frac{2}{5}
1
4
3
−
8
5
2
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Which expression is equivalent to
−
2
2
5
+
(
−
5
1
2
)
-2 \frac{2}{5}+\left(-5 \frac{1}{2}\right)
−
2
5
2
+
(
−
5
2
1
)
?
\newline
−
5
1
2
+
2
2
5
-5 \frac{1}{2}+2 \frac{2}{5}
−
5
2
1
+
2
5
2
\newline
2
2
5
+
(
−
5
1
2
)
2 \frac{2}{5}+\left(-5 \frac{1}{2}\right)
2
5
2
+
(
−
5
2
1
)
\newline
−
2
2
5
−
5
1
2
-2 \frac{2}{5}-5 \frac{1}{2}
−
2
5
2
−
5
2
1
\newline
−
5
1
2
−
(
−
2
2
5
)
-5 \frac{1}{2}-\left(-2 \frac{2}{5}\right)
−
5
2
1
−
(
−
2
5
2
)
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Which expression has the same value as
−
4
+
1
-4+1
−
4
+
1
?
\newline
−
4
−
(
−
1
)
-4-(-1)
−
4
−
(
−
1
)
\newline
−
1
−
(
−
4
)
-1-(-4)
−
1
−
(
−
4
)
\newline
1
−
(
−
4
)
1-(-4)
1
−
(
−
4
)
\newline
4
+
1
4+1
4
+
1
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Which expression has the same value as
−
3
−
6
-3-6
−
3
−
6
?
\newline
6
−
(
−
3
)
6-(-3)
6
−
(
−
3
)
\newline
−
3
−
(
−
6
)
-3-(-6)
−
3
−
(
−
6
)
\newline
−
6
−
(
−
3
)
-6-(-3)
−
6
−
(
−
3
)
\newline
−
3
+
(
−
6
)
-3+(-6)
−
3
+
(
−
6
)
Get tutor help
Rewrite in simplest terms:
−
2
(
−
10
k
−
1
)
+
10
(
−
3
k
+
4
)
-2(-10 k-1)+10(-3 k+4)
−
2
(
−
10
k
−
1
)
+
10
(
−
3
k
+
4
)
\newline
Answer:
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Rewrite in simplest terms:
2
(
−
5
v
+
5
)
+
4
v
2(-5 v+5)+4 v
2
(
−
5
v
+
5
)
+
4
v
\newline
Answer:
Get tutor help
Which expression has the same value as
6
x
−
4
y
6 x-4 y
6
x
−
4
y
?
\newline
−
4
y
+
(
−
6
x
)
-4 y+(-6 x)
−
4
y
+
(
−
6
x
)
\newline
4
y
−
6
x
4 y-6 x
4
y
−
6
x
\newline
6
x
−
(
−
4
y
)
6 x-(-4 y)
6
x
−
(
−
4
y
)
\newline
6
x
+
(
−
4
y
)
6 x+(-4 y)
6
x
+
(
−
4
y
)
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Which expression has the same value as
−
3
1
2
+
(
−
7
3
5
)
-3 \frac{1}{2}+\left(-7 \frac{3}{5}\right)
−
3
2
1
+
(
−
7
5
3
)
?
\newline
−
3
1
2
−
7
3
5
-3 \frac{1}{2}-7 \frac{3}{5}
−
3
2
1
−
7
5
3
\newline
−
7
3
5
−
(
−
3
1
2
)
-7 \frac{3}{5}-\left(-3 \frac{1}{2}\right)
−
7
5
3
−
(
−
3
2
1
)
\newline
7
3
5
−
(
−
3
1
2
)
7 \frac{3}{5}-\left(-3 \frac{1}{2}\right)
7
5
3
−
(
−
3
2
1
)
\newline
−
3
1
2
−
(
−
7
3
5
)
-3 \frac{1}{2}-\left(-7 \frac{3}{5}\right)
−
3
2
1
−
(
−
7
5
3
)
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Which expression has the same value as
−
1
−
9
-1-9
−
1
−
9
?
\newline
−
1
−
(
−
9
)
-1-(-9)
−
1
−
(
−
9
)
\newline
−
1
+
(
−
9
)
-1+(-9)
−
1
+
(
−
9
)
\newline
−
9
+
1
-9+1
−
9
+
1
\newline
1
+
(
−
9
)
1+(-9)
1
+
(
−
9
)
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Which expression is equivalent to
−
8
1
3
+
(
−
8
1
4
)
-8 \frac{1}{3}+\left(-8 \frac{1}{4}\right)
−
8
3
1
+
(
−
8
4
1
)
?
\newline
8
1
3
+
(
−
8
1
4
)
8 \frac{1}{3}+\left(-8 \frac{1}{4}\right)
8
3
1
+
(
−
8
4
1
)
\newline
−
8
1
4
−
(
−
8
1
3
)
-8 \frac{1}{4}-\left(-8 \frac{1}{3}\right)
−
8
4
1
−
(
−
8
3
1
)
\newline
−
8
1
3
−
8
1
4
-8 \frac{1}{3}-8 \frac{1}{4}
−
8
3
1
−
8
4
1
\newline
−
8
1
4
+
8
1
3
-8 \frac{1}{4}+8 \frac{1}{3}
−
8
4
1
+
8
3
1
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Which expression has the same value as
7
1
6
+
3
2
3
7 \frac{1}{6}+3 \frac{2}{3}
7
6
1
+
3
3
2
?
\newline
−
3
2
3
−
7
1
6
-3 \frac{2}{3}-7 \frac{1}{6}
−
3
3
2
−
7
6
1
\newline
3
2
3
−
7
1
6
3 \frac{2}{3}-7 \frac{1}{6}
3
3
2
−
7
6
1
\newline
7
1
6
−
(
−
3
2
3
)
7 \frac{1}{6}-\left(-3 \frac{2}{3}\right)
7
6
1
−
(
−
3
3
2
)
\newline
3
2
3
+
(
−
7
1
6
)
3 \frac{2}{3}+\left(-7 \frac{1}{6}\right)
3
3
2
+
(
−
7
6
1
)
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Which expression has the same value as
−
9
−
3
-9-3
−
9
−
3
?
\newline
3
−
(
−
9
)
3-(-9)
3
−
(
−
9
)
\newline
−
9
−
(
−
3
)
-9-(-3)
−
9
−
(
−
3
)
\newline
−
3
+
9
-3+9
−
3
+
9
\newline
−
9
+
(
−
3
)
-9+(-3)
−
9
+
(
−
3
)
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Which expression has the same value as
70.4
−
50.9
?
70.4-50.9 ?
70.4
−
50.9
?
\newline
70.4
+
(
−
50.9
)
70.4+(-50.9)
70.4
+
(
−
50.9
)
\newline
−
70.4
+
(
−
50.9
)
-70.4+(-50.9)
−
70.4
+
(
−
50.9
)
\newline
50.9
−
70.4
50.9-70.4
50.9
−
70.4
\newline
−
50.9
+
(
−
70.4
)
-50.9+(-70.4)
−
50.9
+
(
−
70.4
)
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Which expression has the same value as
−
2
−
7
-2-7
−
2
−
7
?
\newline
7
−
(
−
2
)
7-(-2)
7
−
(
−
2
)
\newline
−
2
−
(
−
7
)
-2-(-7)
−
2
−
(
−
7
)
\newline
−
2
+
(
−
7
)
-2+(-7)
−
2
+
(
−
7
)
\newline
2
+
(
−
7
)
2+(-7)
2
+
(
−
7
)
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Which expression is equivalent to
5
1
5
−
(
−
5
1
6
)
5 \frac{1}{5}-\left(-5 \frac{1}{6}\right)
5
5
1
−
(
−
5
6
1
)
?
\newline
5
1
5
+
5
1
6
5 \frac{1}{5}+5 \frac{1}{6}
5
5
1
+
5
6
1
\newline
−
5
1
6
−
5
1
5
-5 \frac{1}{6}-5 \frac{1}{5}
−
5
6
1
−
5
5
1
\newline
5
1
5
−
5
1
6
5 \frac{1}{5}-5 \frac{1}{6}
5
5
1
−
5
6
1
\newline
5
1
6
+
(
−
5
1
5
)
5 \frac{1}{6}+\left(-5 \frac{1}{5}\right)
5
6
1
+
(
−
5
5
1
)
Get tutor help
Which expression is equivalent to
3
1
2
+
(
−
1
2
5
)
3 \frac{1}{2}+\left(-1 \frac{2}{5}\right)
3
2
1
+
(
−
1
5
2
)
?
\newline
−
1
2
5
−
3
1
2
-1 \frac{2}{5}-3 \frac{1}{2}
−
1
5
2
−
3
2
1
\newline
3
1
2
−
(
−
1
2
5
)
3 \frac{1}{2}-\left(-1 \frac{2}{5}\right)
3
2
1
−
(
−
1
5
2
)
\newline
−
1
2
5
+
(
−
3
1
2
)
-1 \frac{2}{5}+\left(-3 \frac{1}{2}\right)
−
1
5
2
+
(
−
3
2
1
)
\newline
3
1
2
−
1
2
5
3 \frac{1}{2}-1 \frac{2}{5}
3
2
1
−
1
5
2
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Which expression is equivalent to
−
5
4
5
−
(
−
7
1
5
)
-5 \frac{4}{5}-\left(-7 \frac{1}{5}\right)
−
5
5
4
−
(
−
7
5
1
)
?
\newline
−
5
4
5
+
7
1
5
-5 \frac{4}{5}+7 \frac{1}{5}
−
5
5
4
+
7
5
1
\newline
−
5
4
5
−
7
1
5
-5 \frac{4}{5}-7 \frac{1}{5}
−
5
5
4
−
7
5
1
\newline
7
1
5
−
(
−
5
4
5
)
7 \frac{1}{5}-\left(-5 \frac{4}{5}\right)
7
5
1
−
(
−
5
5
4
)
\newline
5
4
5
+
7
1
5
5 \frac{4}{5}+7 \frac{1}{5}
5
5
4
+
7
5
1
Get tutor help
Rewrite in simplest terms:
2
(
−
9
h
−
4
)
−
7
h
2(-9 h-4)-7 h
2
(
−
9
h
−
4
)
−
7
h
\newline
Answer:
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For the following equation, find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
.
\newline
y
=
7
x
5
+
2
x
4
y=7 x^{5}+2 x^{4}
y
=
7
x
5
+
2
x
4
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
Perform the operation and simplify the answer fully.
\newline
1
2
5
2
\frac{\frac{1}{2}}{\frac{5}{2}}
2
5
2
1
\newline
Answer:
Get tutor help
Perform the operation and simplify the answer fully.
\newline
2
5
2
7
\frac{\frac{2}{5}}{\frac{2}{7}}
7
2
5
2
\newline
Answer:
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