Answer
$(\frac{3x}{2y}$$)^{3}$
Work Step by Step
Given : $\frac{27x^{3}}{8y^{3}}$
Now, $27=3^{3}$ and $8=2^{3}$
Hence, the expression can be written as : $\frac{3^{3}x^{3}}{2^{3}y^{3}}$
Since $a^{m}b^{m}=$ $(ab)^{m}$,
hence $3^{3}x^{3}=$ $(3x)^{3}$ and $2^{3}y^{3}=$ $(2y)^{3}$
Thus, this becomes : $\frac{(3x)^{3}}{(2y)^{3}}$
This becomes : $(\frac{3x}{2y}$$)^{3}$
(since $\frac{a^{m}}{b^{m}}=$ ($\frac{a}{b}$$)^{m}$)
