perform the indicated operation. write the answer using only positive expon\\(\\left(\\dfrac{64}{27}\\right)^…

perform the indicated operation. write the answer using only positive expon\\(\\left(\\dfrac{64}{27}\\right)^{-4/3}\\)\\(\\left(\\dfrac{64}{27}\\right)^{-4/3}=\\square\\) (simplify your answer.)

perform the indicated operation. write the answer using only positive expon\\(\\left(\\dfrac{64}{27}\\right)^{-4/3}\\)\\(\\left(\\dfrac{64}{27}\\right)^{-4/3}=\\square\\) (simplify your answer.)

Answer

Explanation:

Step1: Flip base for negative exponent

$\left(\frac{64}{27}\right)^{-4/3} = \left(\frac{27}{64}\right)^{4/3}$

Step2: Rewrite as root and power

$\left(\frac{27}{64}\right)^{4/3} = \left(\sqrt[3]{\frac{27}{64}}\right)^4$

Step3: Compute cube root

$\sqrt[3]{\frac{27}{64}} = \frac{3}{4}$, since $3^3=27$ and $4^3=64$

Step4: Raise to 4th power

$\left(\frac{3}{4}\right)^4 = \frac{3^4}{4^4} = \frac{81}{256}$

Answer:

$\frac{81}{256}$