The value of \(\displaystyle\left(\frac{8}{125}\right)^{-\frac{4}{3}}\) is __________
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{625}{16}\)
A negative power turns the fraction upside down, and the power \(\frac{4}{3}\) means: take the cube root, then raise it to the 4th power.
\(\displaystyle \left(\frac{8}{125}\right)^{-\frac{4}{3}}=\left(\frac{125}{8}\right)^{\frac{4}{3}}\)
\(\displaystyle \left(\frac{125}{8}\right)^{\frac{1}{3}}=\frac{5}{2}\), since \(5^{3}=125\) and \(2^{3}=8\)
\(\displaystyle \left(\frac{5}{2}\right)^{4}=\frac{625}{16}\)