Simplify the expression involving rational exponents.
-$\left(\frac{64}{729}\right)^{-2 / 3}$

A) $\frac{81}{16}$

B) $\frac{729}{64}$

C) $\frac{16}{81}$

D) $\frac{64}{729}$

Question

Simplify the expression involving rational exponents.
-$\left(\frac{64}{729}\right)^{-2 / 3}$

A) $\frac{81}{16}$

B) $\frac{729}{64}$

C) $\frac{16}{81}$

D) $\frac{64}{729}$

Quizplus · Accepted Answer

The expression $\left(\frac{64}{729}\right)^{-2 / 3}$ can be simplified by first converting the negative exponent to a positive one by taking the reciprocal of the base, which gives $\left(\frac{729}{64}\right)^{2 / 3}$. Then, taking the cube root (due to the denominator of the exponent) of both the numerator and the denominator gives $9^2 / 4^2$, which simplifies to $\frac{81}{16}$.

Simplify the Expression Involving Rational Exponents (64729)−2/3\left(\frac{64}{729}\right)^{-2 / 3}(72964​)−2/3 A) 8116\frac{81}{16}1681​ B) 72964\frac{729}{64}64729​

Simplify the Expression Involving Rational Exponents $\left(\frac{64}{729}\right)^{-2 / 3}$ A) $\frac{81}{16}$ B) $\frac{729}{64}$