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Mathematics
Problem
Simplify the following expression so that the final answer is written as a product of powers of the primes
2
2
2
and
3
3
3
and of the variables
x
x
x
and
y
y
y
, each with positive integer exponents only:
(
18
x
3
y
−
2
)
3
4
(
12
x
−
5
y
4
)
1
2
(
3
x
−
2
y
)
−
3
2
×
(
27
x
6
8
y
3
)
1
4
.
\frac{(18x^{3}y^{-2})^{\tfrac{3}{4}}\,(12x^{-5}y^{4})^{\tfrac{1}{2}}}{(3x^{-2}y)^{-\tfrac{3}{2}}}\times\left(\frac{27x^{6}}{8y^{3}}\right)^{\tfrac{1}{4}}.
(
3
x
−
2
y
)
−
2
3
(
18
x
3
y
−
2
)
4
3
(
12
x
−
5
y
4
)
2
1
×
(
8
y
3
27
x
6
)
4
1
.
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