Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers.
-$\left(\frac{9 x^{2}}{y^{2}}\right)^{3}\left(\frac{15 x^{2}}{y^{-4}}\right)^{-2}$

A) $\frac{81 x^{2}}{25 y^{14}}$

B) $\frac{81 x^{2} y^{14}}{5}$

C) $\frac{25 x^{3}}{9 y^{14}}$

D) $-\frac{27 x}{25 y^{10}}$

Question

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers.
-$\left(\frac{9 x^{2}}{y^{2}}\right)^{3}\left(\frac{15 x^{2}}{y^{-4}}\right)^{-2}$

A) $\frac{81 x^{2}}{25 y^{14}}$

B) $\frac{81 x^{2} y^{14}}{5}$

C) $\frac{25 x^{3}}{9 y^{14}}$

D) $-\frac{27 x}{25 y^{10}}$

Quizplus · Accepted Answer

First, simplify each part separately: $\left(\frac{9 x^{2}}{y^{2}}\right)^{3} = \frac{729 x^{6}}{y^{6}}$ and $\left(\frac{15 x^{2}}{y^{-4}}\right)^{-2} = \left(\frac{y^{4}}{15 x^{2}}\right)^{2} = \frac{y^{8}}{225 x^{4}}$. Multiplying these together gives $\frac{729 x^{6}}{y^{6}} \cdot \frac{y^{8}}{225 x^{4}} = \frac{729}{225} \cdot \frac{x^{6}}{x^{4}} \cdot \frac{y^{8}}{y^{6}} = \frac{81 x^{2}}{25 y^{14}}$.

Simplify Write the Answer with Only Positive Exponents (9x2y2)3(15x2y−4)−2\left(\frac{9 x^{2}}{y^{2}}\right)^{3}\left(\frac{15 x^{2}}{y^{-4}}\right)^{-2}(y29x2​)3(y−415x2​)−2

Simplify Write the Answer with Only Positive Exponents $\left(\frac{9 x^{2}}{y^{2}}\right)^{3}\left(\frac{15 x^{2}}{y^{-4}}\right)^{-2}$