Simplify
x^-2y^10z^-8/(x^3 y^2 z^3)^4 *
(x^3 y^2) (3xy^5)^2/9x4 y9
Answers
Answer:
Move
(
x
−
2
y
2
)
−
4
to the numerator using the negative exponent rule
1
b
−
n
=
b
n
.
(
(
3
x
y
−
5
)
3
(
x
−
2
y
2
)
4
)
−
2
Rewrite the expression using the negative exponent rule
b
−
n
=
1
b
n
.
(
(
3
x
1
y
5
)
3
(
x
−
2
y
2
)
4
)
−
2
Multiply
3
x
1
y
5
.
Tap for more steps...
(
(
x
⋅
3
y
5
)
3
(
x
−
2
y
2
)
4
)
−
2
Move
3
to the left of
x
.
(
(
3
⋅
x
y
5
)
3
(
x
−
2
y
2
)
4
)
−
2
Use the power rule
(
a
b
)
n
=
a
n
b
n
to distribute the exponent.
Tap for more steps...
(
3
3
x
3
(
y
5
)
3
(
x
−
2
y
2
)
4
)
−
2
Raise
3
to the power of
3
.
(
27
x
3
(
y
5
)
3
(
x
−
2
y
2
)
4
)
−
2
Multiply the exponents in
(
y
5
)
3
.
Tap for more steps...
(
27
x
3
y
15
(
x
−
2
y
2
)
4
)
−
2
Rewrite the expression using the negative exponent rule
b
−
n
=
1
b
n
.
(
27
x
3
y
15
(
1
x
2
y
2
)
4
)
−
2
Combine
1
x
2
and
y
2
.
(
27
x
3
y
15
(
y
2
x
2
)
4
)
−
2
Apply basic rules of exponents.
Tap for more steps...
(
27
x
3
y
15
⋅
y
8
x
8
)
−
2
Cancel the common factor of
x
3
.
Tap for more steps...
(
27
y
15
⋅
y
8
x
5
)
−
2
Cancel the common factor of
y
8
.
Tap for more steps...
(
27
y
7
⋅
1
x
5
)
−
2
Multiply
27
y
7
and
1
x
5
.
(
27
y
7
x
5
)
−
2
Change the sign of the exponent by rewriting the base as its reciprocal.
(
y
7
x
5
27
)
2
Use the power rule
(
a
b
)
n
=
a
n
b
n
to distribute the exponent.
Tap for more steps...
(
y
7
)
2
(
x
5
)
2
27
2
Simplify the numerator.
Tap for more steps...
y
14
x
10
27
2
Raise
27
to the power of
2
.
y
14
x
10
729
()