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Math Problems
Algebra 1
Negative exponents
Which is equal to
1
2
86
\frac{1}{2^{86}}
2
86
1
?
\newline
Choices:
\newline
(A)
−
(
−
2
)
86
-(-2)^{86}
−
(
−
2
)
86
\newline
(B)
1
(
−
2
)
−
86
\frac{1}{(-2)^{-86}}
(
−
2
)
−
86
1
\newline
(C)
−
1
2
−
86
-\frac{1}{2^{-86}}
−
2
−
86
1
\newline
(D)
2
−
86
2^{-86}
2
−
86
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
9
0
87
\frac{1}{90^{87}}
9
0
87
1
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Which is equal to
1
5
4
6
\frac{1}{54^6}
5
4
6
1
?
\newline
Choices:
\newline
(A)
5
4
−
6
54^{-6}
5
4
−
6
\newline
(B)
1
5
4
−
6
\frac{1}{54^{-6}}
5
4
−
6
1
\newline
(C)
−
1
(
−
54
)
−
6
-\frac{1}{(-54)^{-6}}
−
(
−
54
)
−
6
1
\newline
(D)
1
(
−
54
)
−
6
\frac{1}{(-54)^{-6}}
(
−
54
)
−
6
1
Get tutor help
Which is equal to
1
5
15
\frac{1}{5^{15}}
5
15
1
?
\newline
Choices:
\newline
(A)
5
−
15
5^{-15}
5
−
15
\newline
(B)
1
(
−
5
)
15
\frac{1}{(-5)^{15}}
(
−
5
)
15
1
\newline
(C)
(
−
5
)
15
(-5)^{15}
(
−
5
)
15
\newline
(D)
−
(
−
5
)
15
-(-5)^{15}
−
(
−
5
)
15
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
6
6
2
\frac{1}{66^2}
6
6
2
1
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
7
28
\frac{1}{7^{28}}
7
28
1
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Which is equal to
1
3
98
\frac{1}{3^{98}}
3
98
1
?
\newline
Choices:
\newline
(A)
−
(
−
3
)
98
-(-3)^{98}
−
(
−
3
)
98
\newline
(B)
−
1
(
−
3
)
−
98
-\frac{1}{(-3)^{-98}}
−
(
−
3
)
−
98
1
\newline
(C)
1
3
−
98
\frac{1}{3^{-98}}
3
−
98
1
\newline
(D)
3
−
98
3^{-98}
3
−
98
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
2
2
6
\frac{1}{22^6}
2
2
6
1
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
7
61
\frac{1}{7^{61}}
7
61
1
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Which is equal to
1
1
7
7
\frac{1}{17^7}
1
7
7
1
?
\newline
Choices:
\newline
(A)
−
(
−
17
)
7
-(-17)^7
−
(
−
17
)
7
\newline
(B)
1
1
7
−
7
\frac{1}{17^{-7}}
1
7
−
7
1
\newline
(C)
1
7
−
7
17^{-7}
1
7
−
7
\newline
(D)
−
1
(
−
17
)
−
7
-\frac{1}{(-17)^{-7}}
−
(
−
17
)
−
7
1
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Write the expression as a fraction with a positive exponent. Do not evaluate the expression.
\newline
1
8
14
\frac{1}{8^{14}}
8
14
1
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
9
4
\frac{1}{9^4}
9
4
1
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Write the expression as a fraction with a positive exponent. Do not evaluate the expression.
\newline
1
4
30
\frac{1}{4^{30}}
4
30
1
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
7
2
\frac{1}{7^2}
7
2
1
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
3
16
\frac{1}{3^{16}}
3
16
1
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
1
6
72
\frac{1}{16^{72}}
1
6
72
1
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
9
96
\frac{1}{9^{96}}
9
96
1
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Which is equal to
1
6
94
\frac{1}{6^{94}}
6
94
1
?
\newline
Choices:
\newline
(A)
6
−
94
6^{-94}
6
−
94
\newline
(B)
1
(
−
6
)
−
94
\frac{1}{(-6)^{-94}}
(
−
6
)
−
94
1
\newline
(C)
6
94
6^{94}
6
94
\newline
(D)
−
1
6
−
94
-\frac{1}{6^{-94}}
−
6
−
94
1
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Which is equal to
1
8
4
2
\frac{1}{84^2}
8
4
2
1
?
\newline
Choices:
\newline
(A)
(
−
84
)
2
(-84)^2
(
−
84
)
2
\newline
(B)
−
8
4
2
-84^2
−
8
4
2
\newline
(C)
8
4
−
2
84^{-2}
8
4
−
2
\newline
(D)
1
8
4
−
2
\frac{1}{84^{-2}}
8
4
−
2
1
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Which is equal to
1
4
44
\frac{1}{4^{44}}
4
44
1
?
\newline
Choices:
\newline
(A)
−
1
4
−
44
-\frac{1}{4^{-44}}
−
4
−
44
1
\newline
(B)
(
−
4
)
44
(-4)^{44}
(
−
4
)
44
\newline
(C)
4
−
44
4^{-44}
4
−
44
\newline
(D)
−
4
44
-4^{44}
−
4
44
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Which is equal to
1
7
10
\frac{1}{7^{10}}
7
10
1
?
\newline
Choices:
\newline
(A)
(
−
7
)
10
(-7)^{10}
(
−
7
)
10
\newline
(B)
−
7
10
-7^{10}
−
7
10
\newline
(C)
7
−
10
7^{-10}
7
−
10
\newline
(D)
−
1
7
−
10
-\frac{1}{7^{-10}}
−
7
−
10
1
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Write the expression as a fraction with a positive exponent. Do not evaluate the expression.
\newline
1
8
−
4
\frac{1}{8^{-4}}
8
−
4
1
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Which is equal to
5
6
−
82
56^{-82}
5
6
−
82
?
\newline
Choices:
\newline
(A)
(
−
56
)
82
(-56)^{82}
(
−
56
)
82
\newline
(B)
1
5
6
82
\frac{1}{56^{82}}
5
6
82
1
\newline
(C)
5
6
82
56^{82}
5
6
82
\newline
(D)
1
5
6
−
82
\frac{1}{56^{-82}}
5
6
−
82
1
Get tutor help
Which is equal to
1
5
4
5
\frac{1}{54^5}
5
4
5
1
?
\newline
Choices:
\newline
(A)
−
5
4
5
-54^5
−
5
4
5
\newline
(B)
(
−
54
)
5
(-54)^5
(
−
54
)
5
\newline
(C)
5
4
−
5
54^{-5}
5
4
−
5
\newline
(D)
−
1
5
4
−
5
-\frac{1}{54^{-5}}
−
5
4
−
5
1
Get tutor help
Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
4
7
\frac{1}{4^7}
4
7
1
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Write the expression as a fraction with a positive exponent. Do not evaluate the expression.
\newline
1
5
13
\frac{1}{5^{13}}
5
13
1
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
1
6
8
\frac{1}{16^8}
1
6
8
1
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
8
3
3
\frac{1}{83^3}
8
3
3
1
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Which is equal to
1
6
92
\frac{1}{6^{92}}
6
92
1
?
\newline
Choices:
\newline
(A)
−
1
6
−
92
-\frac{1}{6^{-92}}
−
6
−
92
1
\newline
(B)
6
92
6^{92}
6
92
\newline
(C)
6
−
92
6^{-92}
6
−
92
\newline
(D)
−
1
(
−
6
)
−
92
-\frac{1}{(-6)^{-92}}
−
(
−
6
)
−
92
1
Get tutor help
Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
9
0
2
\frac{1}{90^2}
9
0
2
1
Get tutor help
Which is equal to
1
9
1
9
\frac{1}{91^9}
9
1
9
1
?
\newline
Choices:
\newline
(A)
9
1
−
9
91^{-9}
9
1
−
9
\newline
(B)
9
1
9
91^9
9
1
9
\newline
(C)
1
(
−
91
)
−
9
\frac{1}{(-91)^{-9}}
(
−
91
)
−
9
1
\newline
(D)
(
−
91
)
9
(-91)^9
(
−
91
)
9
Get tutor help
Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
8
4
8
\frac{1}{84^8}
8
4
8
1
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Write the expression as a fraction with a positive exponent. Do not evaluate the expression.
\newline
1
6
4
36
\frac{1}{64^{36}}
6
4
36
1
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Write the expression as a fraction with a positive exponent. Do not evaluate the expression.
\newline
1
6
17
\frac{1}{6^{17}}
6
17
1
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
1
5
60
\frac{1}{15^{60}}
1
5
60
1
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Which is equal to
1
9
25
\frac{1}{9^{25}}
9
25
1
?
\newline
Choices:
\newline
(A)
−
9
25
-9^{25}
−
9
25
\newline
(B)
1
(
−
9
)
−
25
\frac{1}{(-9)^{-25}}
(
−
9
)
−
25
1
\newline
(C)
−
(
−
9
)
25
-(-9)^{25}
−
(
−
9
)
25
\newline
(D)
9
−
25
9^{-25}
9
−
25
Get tutor help
Write the expression as a fraction with a positive exponent. Do not evaluate the expression.
\newline
1
4
7
16
\frac{1}{47^{16}}
4
7
16
1
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
2
4
6
\frac{1}{24^6}
2
4
6
1
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
9
3
69
\frac{1}{93^{69}}
9
3
69
1
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Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
5
20
\frac{1}{5^{20}}
5
20
1
Get tutor help
Which is equal to
3
−
25
3^{-25}
3
−
25
?
\newline
Choices:
\newline
(A)
1
3
25
\frac{1}{3^{25}}
3
25
1
\newline
(B)
(
−
3
)
25
(-3)^{25}
(
−
3
)
25
\newline
(C)
1
3
−
25
\frac{1}{3^{-25}}
3
−
25
1
\newline
(D)
(
−
3
)
−
25
(-3)^{-25}
(
−
3
)
−
25
Get tutor help
Write the expression as a whole number with a negative exponent. Do not evaluate the expression.
\newline
1
6
6
8
\frac{1}{66^8}
6
6
8
1
Get tutor help
Is
8
\sqrt{8}
8
a real number?
\newline
Choices:
\newline
(A) yes
\newline
(B) no
Get tutor help
Simplify
−
27
\sqrt{-27}
−
27
.
\newline
If the answer is radical use
5
\sqrt{5}
5
to denote
5
\sqrt{5}
5
(use the correct radicand in the problem)
\newline
If the answer is complex use
i
i
i
.
Get tutor help
f
(
x
)
=
{
−
5
for
x
<
3
2
for
x
=
3
−
(
x
−
4
)
2
+
5
for
x
>
3
f(x)=\left\{\begin{array}{lll} -5 & \text { for } & x<3 \\ 2 & \text { for } & x=3 \\ -(x-4)^{2}+5 & \text { for } & x>3 \end{array}\right.
f
(
x
)
=
⎩
⎨
⎧
−
5
2
−
(
x
−
4
)
2
+
5
for
for
for
x
<
3
x
=
3
x
>
3
\newline
Find
f
(
2
)
f(2)
f
(
2
)
\newline
Answer:
\newline
Get tutor help
f
(
x
)
=
{
(
x
+
1
)
2
−
8
for
x
≠
−
4
3
for
x
=
−
4
f(x)=\left\{\begin{array}{lll} (x+1)^{2}-8 & \text { for } & x \neq-4 \\ 3 & \text { for } & x=-4 \end{array}\right.
f
(
x
)
=
{
(
x
+
1
)
2
−
8
3
for
for
x
=
−
4
x
=
−
4
\newline
Find
f
(
−
1
)
f(-1)
f
(
−
1
)
\newline
Answer:
\newline
Get tutor help
f
(
x
)
=
{
−
(
x
+
6
)
2
−
2
for
x
≤
−
5
−
6
x
−
14
for
x
>
−
2
f(x)=\left\{\begin{array}{lll} -(x+6)^{2}-2 & \text { for } & x \leq-5 \\ -6 x-14 & \text { for } & x>-2 \end{array}\right.
f
(
x
)
=
{
−
(
x
+
6
)
2
−
2
−
6
x
−
14
for
for
x
≤
−
5
x
>
−
2
\newline
Find
f
(
−
5
)
f(-5)
f
(
−
5
)
\newline
Answer:
\newline
Get tutor help
f
(
x
)
=
{
−
(
x
−
2
)
2
+
3
for
x
<
2
−
3
for
x
=
2
−
2
x
+
7
for
2
<
x
≤
6
f(x)=\left\{\begin{array}{lll} -(x-2)^{2}+3 & \text { for } & x<2 \\ -3 & \text { for } & x=2 \\ -2 x+7 & \text { for } & 2<x \leq 6 \end{array}\right.
f
(
x
)
=
⎩
⎨
⎧
−
(
x
−
2
)
2
+
3
−
3
−
2
x
+
7
for
for
for
x
<
2
x
=
2
2
<
x
≤
6
\newline
Find
f
(
4
)
f(4)
f
(
4
)
\newline
Answer:
\newline
Get tutor help
Solve the equation. Check your solution
\newline
1
4
(
−
16
k
+
52
)
=
8
+
10
k
\frac{1}{4}(-16k+52)=8+10k
4
1
(
−
16
k
+
52
)
=
8
+
10
k
\newline
Get tutor help
Find the average value of the function
f
(
x
)
=
6
3
−
4
x
f(x)=\frac{6}{3-4 x}
f
(
x
)
=
3
−
4
x
6
from
x
=
1
x=1
x
=
1
to
x
=
7
x=7
x
=
7
. Express your answer as a constant times
ln
5
\ln 5
ln
5
.
\newline
Answer:
□
ln
5
\square\ln 5
□
ln
5
Get tutor help
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