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Let’s check out your problem:
(
−
2
x
2
y
7
)
5
\left(-2 x^{2} y^{7}\right)^{5}
(
−
2
x
2
y
7
)
5
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Math Problems
Algebra 2
Evaluate rational exponents
Full solution
Q.
(
−
2
x
2
y
7
)
5
\left(-2 x^{2} y^{7}\right)^{5}
(
−
2
x
2
y
7
)
5
Identify base and exponent:
Identify the base and the exponent in the expression.
(
−
2
x
2
y
7
)
5
(-2x^{2}y^{7})^{5}
(
−
2
x
2
y
7
)
5
has a base of
−
2
x
2
y
7
-2x^{2}y^{7}
−
2
x
2
y
7
and an exponent of
5
5
5
.
Apply power of product rule:
Apply the power of a product rule:
(
a
b
)
n
=
a
n
∗
b
n
(ab)^n = a^n * b^n
(
ab
)
n
=
a
n
∗
b
n
.
(
−
2
x
2
y
7
)
5
=
(
−
2
)
5
∗
(
x
2
)
5
∗
(
y
7
)
5
(-2x^{2}y^{7})^5 = (-2)^5 * (x^2)^5 * (y^7)^5
(
−
2
x
2
y
7
)
5
=
(
−
2
)
5
∗
(
x
2
)
5
∗
(
y
7
)
5
.
Calculate each part:
Calculate each part:
\newline
(
−
2
)
5
=
−
32
(-2)^5 = -32
(
−
2
)
5
=
−
32
,
\newline
(
x
2
)
5
=
x
(
2
∗
5
)
=
x
10
(x^2)^5 = x^{(2*5)} = x^{10}
(
x
2
)
5
=
x
(
2
∗
5
)
=
x
10
,
\newline
(
y
7
)
5
=
y
(
7
∗
5
)
=
y
35
(y^7)^5 = y^{(7*5)} = y^{35}
(
y
7
)
5
=
y
(
7
∗
5
)
=
y
35
.
Combine results:
Combine the results:
\newline
−
32
×
x
10
×
y
35
-32 \times x^{10} \times y^{35}
−
32
×
x
10
×
y
35
.
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or
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or
A
B
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, where
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A
and
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