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Math Problems
Grade 8
Evaluate expressions using properties of exponents
Simplify.
\newline
Rewrite the expression in the form
\newline
z
n
z^{n}
z
n
.
\newline
z
7
z
−
14
\frac{z^{7}}{z^{-14}}
z
−
14
z
7
=
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Simplify.
\newline
Rewrite the expression in the form
\newline
9
n
9^{n}
9
n
.
\newline
(
9
−
3
)
(
9
12
)
=
(9^{-3})(9^{12})=
(
9
−
3
)
(
9
12
)
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
y
n
y^{n}
y
n
.
\newline
y
−
7
y
−
13
\frac{y^{-7}}{y^{-13}}
y
−
13
y
−
7
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
a
n
a^{n}
a
n
.
\newline
a
−
13
a
−
6
=
\frac{a^{-13}}{a^{-6}}=
a
−
6
a
−
13
=
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Simplify.
\newline
Rewrite the expression in the form
\newline
5
n
5^n
5
n
.
\newline
5
−
5
5
8
=
\frac{5^{-5}}{5^8}=
5
8
5
−
5
=
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Simplify.
\newline
Rewrite the expression in the form
\newline
8
n
8^{n}
8
n
.
\newline
(
8
−
8
)
(
8
3
)
=
(8^{-8})(8^{3})=
(
8
−
8
)
(
8
3
)
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
x
(
n
)
.
x^{(n)}.
x
(
n
)
.
\newline
x
(
2
)
⋅
x
(
−
12
)
=
x^{(2)}\cdot x^{(-12)}=
x
(
2
)
⋅
x
(
−
12
)
=
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
4
n
4^{n}
4
n
.
\newline
4
11
4
−
8
=
\frac{4^{11}}{4^{-8}}=
4
−
8
4
11
=
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Select the equivalent expression.
\newline
(
2
−
7
⋅
5
5
)
2
=
(2^{-7}\cdot5^{5})^{2}=
(
2
−
7
⋅
5
5
)
2
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
−
14
⋅
5
10
2^{-14}\cdot5^{10}
2
−
14
⋅
5
10
\newline
(B)
2
−
5
⋅
5
7
2^{-5}\cdot5^{7}
2
−
5
⋅
5
7
\newline
(C)
2
−
7
⋅
5
10
2^{-7}\cdot5^{10}
2
−
7
⋅
5
10
Get tutor help
Simplify.
\newline
Rewrite the expression in the form
\newline
a
n
a^{n}
a
n
.
\newline
a
5
⋅
a
−
3
=
a^{5} \cdot a^{-3} =
a
5
⋅
a
−
3
=
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Select the equivalent expression.
\newline
(
5
4
⋅
b
−
10
)
−
6
=
(5^{4}\cdot b^{-10})^{-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
Get tutor help
Select the equivalent expression.
\newline
(
4
3
5
−
2
)
5
=
?
\left(\frac{4^{3}}{5^{-2}}\right)^{5}=\,?
(
5
−
2
4
3
)
5
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
8
5
3
\frac{4^{8}}{5^{3}}
5
3
4
8
\newline
(B)
4
15
5
10
\frac{4^{15}}{5^{10}}
5
10
4
15
\newline
(C)
4
15
⋅
5
10
4^{15}\cdot 5^{10}
4
15
⋅
5
10
Get tutor help
Select the equivalent expression.
\newline
(
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
3
3
−
30
\frac{7^{3}}{3^{-30}}
3
−
30
7
3
\newline
(B)
7
15
3
30
\frac{7^{15}}{3^{30}}
3
30
7
15
\newline
(C)
3
15
7
30
\frac{3^{15}}{7^{30}}
7
30
3
15
Get tutor help
Select the equivalent expression.
\newline
(
x
−
3
y
3
)
−
7
=
(x^{-3}y^{3})^{-7}=
(
x
−
3
y
3
)
−
7
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
\newline
x
21
y
−
21
x^{21}y^{-21}
x
21
y
−
21
\newline
(B)
\newline
(
x
y
)
0
(xy)^{0}
(
x
y
)
0
\newline
(C)
\newline
x
−
10
y
−
4
x^{-10}y^{-4}
x
−
10
y
−
4
Get tutor help
Select the equivalent expression.
\newline
(
2
−
4
⋅
z
−
3
)
5
=
(2^{-4} \cdot z^{-3})^{5}=
(
2
−
4
⋅
z
−
3
)
5
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
z
2
2z^{2}
2
z
2
\newline
(B)
2
20
⋅
z
15
2^{20} \cdot z^{15}
2
20
⋅
z
15
\newline
(C)
1
2
20
⋅
z
15
\frac{1}{2^{20} \cdot z^{15}}
2
20
⋅
z
15
1
Get tutor help
Select the equivalent expression.
\newline
(
a
−
3
b
2
)
4
=
?
\left(\frac{a^{-3}}{b^{2}}\right)^{4}=\,?
(
b
2
a
−
3
)
4
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
b
2
a
7
\frac{b^{2}}{a^{7}}
a
7
b
2
\newline
(B)
1
a
12
b
8
\frac{1}{a^{12}b^{8}}
a
12
b
8
1
\newline
(C)
(
b
a
)
20
\left(\frac{b}{a}\right)^{20}
(
a
b
)
20
Get tutor help
Select the equivalent expression.
\newline
(
(
2
−
10
)
/
(
4
2
)
)
7
=
?
((2^{-10})/(4^{2}))^{7}=?
((
2
−
10
)
/
(
4
2
)
)
7
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
\newline
(
1
)
/
(
2
70
⋅
4
14
)
(1)/(2^{70}\cdot4^{14})
(
1
)
/
(
2
70
⋅
4
14
)
\newline
(B)
\newline
2
84
2^{84}
2
84
\newline
(C)
\newline
2
−
3
⋅
4
−
9
2^{-3}\cdot4^{-9}
2
−
3
⋅
4
−
9
Get tutor help
Select the equivalent expression.
\newline
(
(
x
4
)
/
(
7
−
8
)
)
−
7
=
((x^{4})/(7^{-8}))^{-7}=
((
x
4
)
/
(
7
−
8
)
)
−
7
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
\newline
x
−
28
⋅
7
56
x^{-28}\cdot7^{56}
x
−
28
⋅
7
56
\newline
(B)
\newline
(
x
28
)
/
(
7
56
)
(x^{28})/(7^{56})
(
x
28
)
/
(
7
56
)
\newline
(C)
\newline
(
x
28
)
/
(
7
−
56
)
(x^{28})/(7^{-56})
(
x
28
)
/
(
7
−
56
)
Get tutor help
Select the equivalent expression.
\newline
(
a
−
7
b
−
2
)
−
9
=
(a^{-7}b^{-2})^{-9}=
(
a
−
7
b
−
2
)
−
9
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
a
63
b
18
\frac{a^{63}}{b^{18}}
b
18
a
63
\newline
(B)
b
18
a
63
\frac{b^{18}}{a^{63}}
a
63
b
18
\newline
(C)
a
63
b
18
a^{63}b^{18}
a
63
b
18
Get tutor help
Select the equivalent expression.
\newline
(
a
−
2
⋅
8
7
)
2
=
(a^{-2}\cdot 8^{7})^{2}=
(
a
−
2
⋅
8
7
)
2
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
(
8
a
)
10
(8a)^{10}
(
8
a
)
10
\newline
(B)
a
−
4
⋅
8
14
a^{-4}\cdot 8^{14}
a
−
4
⋅
8
14
\newline
(C)
8
9
8^{9}
8
9
Get tutor help
Select the equivalent expression.
\newline
(
3
−
8
⋅
7
3
)
−
2
=
(3^{-8}\cdot7^{3})^{-2}=
(
3
−
8
⋅
7
3
)
−
2
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
7
6
3
16
\frac{7^{6}}{3^{16}}
3
16
7
6
\newline
(B)
2
1
10
21^{10}
2
1
10
\newline
(C)
3
16
⋅
7
−
6
3^{16}\cdot7^{-6}
3
16
⋅
7
−
6
Get tutor help
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
Get tutor help
Select the equivalent expression.
\newline
(
(
8
−
5
)
/
(
2
−
2
)
)
−
4
=
?
((8^{-5})/(2^{-2}))^{-4}=?
((
8
−
5
)
/
(
2
−
2
)
)
−
4
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
\newline
(
8
20
)
/
(
2
8
)
(8^{20})/(2^{8})
(
8
20
)
/
(
2
8
)
\newline
(B)
\newline
(
2
6
)
/
(
8
9
)
(2^{6})/(8^{9})
(
2
6
)
/
(
8
9
)
\newline
(C)
\newline
(
1
)
/
(
8
⋅
2
2
)
(1)/(8\cdot 2^{2})
(
1
)
/
(
8
⋅
2
2
)
Get tutor help
Select the equivalent expression.
\newline
(
b
7
4
5
)
−
3
=
?
\left(\frac{b^{7}}{4^{5}}\right)^{-3}=\,?
(
4
5
b
7
)
−
3
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
b
21
4
15
\frac{b^{21}}{4^{15}}
4
15
b
21
\newline
(B)
4
15
b
21
\frac{4^{15}}{b^{21}}
b
21
4
15
\newline
(C)
b
−
21
⋅
4
−
15
b^{-21}\cdot 4^{-15}
b
−
21
⋅
4
−
15
Get tutor help
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