Find the value of left(frac{125}{64}right)^{- | vedclass

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Question

(A) Given expression: $\left(\frac{125}{64}\right)^{-\frac{2}{3}}$First,we use the property $(a/b)^{-n} = (b/a)^n$ to remove the negative exponent:$\l

Vedclass · Accepted Answer

$\frac{16}{25}$

Vedclass · Answer

(A) Given expression: $\left(\frac{125}{64}\right)^{-\frac{2}{3}}$First,we use the property $(a/b)^{-n} = (b/a)^n$ to remove the negative exponent:$\left(\frac{64}{125}\right)^{\frac{2}{3}}$Next,express $64$ as $4^3$ and $125$ as $5^3$:$\left(\frac{4^3}{5^3}\right)^{\frac{2}{3}} = \left(\left(\frac{4}{5}\right)^3\right)^{\frac{2}{3}}$Using the power rule $(x^a)^b = x^{a \cdot b}$:$\left(\frac{4}{5}\right)^{3 \cdot \frac{2}{3}} = \left(\frac{4}{5}\right)^2$Finally,calculate the square:$\frac{4^2}{5^2} = \frac{16}{25}$

Find the value of $\left(\frac{125}{64}\right)^{-\frac{2}{3}}$.

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