Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers.
-$\frac{\left(2 x^{2} y^{5}\right)^{-1}}{\left(3 x^{2} y^{3}\right)^{3}}$

A) $\frac{2}{27 x^{8} y^{14}}$

B) $\frac{1}{54 x^{8} y^{14}}$

C) $54 x^{8} y^{14}$

D) $\frac{1}{54 x^{4} y^{4}}$

Question

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers.
-$\frac{\left(2 x^{2} y^{5}\right)^{-1}}{\left(3 x^{2} y^{3}\right)^{3}}$

A) $\frac{2}{27 x^{8} y^{14}}$

B) $\frac{1}{54 x^{8} y^{14}}$

C) $54 x^{8} y^{14}$

D) $\frac{1}{54 x^{4} y^{4}}$

Quizplus · Accepted Answer

First, simplify the numerator and denominator separately. The numerator becomes $2^{-1}x^{-2}y^{-5}$ and the denominator becomes $27x^{6}y^{9}$. When dividing, subtract the exponents of like bases, resulting in $2^{-1}27^{-1}x^{-8}y^{-14}$, which simplifies to $\frac{1}{54 x^{8} y^{14}}$.

Simplify Write the Answer with Only Positive Exponents (2x2y5)−1(3x2y3)3\frac{\left(2 x^{2} y^{5}\right)^{-1}}{\left(3 x^{2} y^{3}\right)^{3}}(3x2y3)3(2x2y5)−1​

Simplify Write the Answer with Only Positive Exponents $\frac{\left(2 x^{2} y^{5}\right)^{-1}}{\left(3 x^{2} y^{3}\right)^{3}}$