Question

Which of these expresses $\sqrt[3]{3{64}^{-4}}$ in the simplest form?

• A. 256
• B. $\frac{1}{256}$
• C. 16
• D. $\frac{1}{16}$

Answer 1

The correct option is B $\frac{1}{256}$

$\sqrt[3]{3{64}^{-4}}=({64}^{-4}{)}^{\frac{1}{3}}$
$=\left({64}^{-4}{)}^{-4\times \frac{1}{3}}\text{[}(a^m{)}^n=a^{mn}\right]$
$=(4^3{)}^{\frac{-4}{3}}$
$=4^{-4}\text{[}(a^m{)}^n=a^{mn}]$
$=\frac{1}{4^4}[a^{-m}=\frac{1}{a^m}]$
$=\frac{1}{256}$
So, option (2) is correct