Question

The expression 8^-2/3 is equivalent to?

Answer 1

$Use:\\a^{-n}=\left(\frac{1}{a}\right)^n\\\\a^\frac{m}{n}=(\sqrt[n]{a})^m\\\\8^{-\frac{2}{3}}=\left(\frac{1}{8}\right)^\frac{2}{3}=\left(\sqrt[3]{\frac{1}{8}}\right)^2=\left(\frac{1}{2}\right)^2=\boxed{\frac{1}{4}}$


$or\ use:\\\\\left(a^n\right)^m=a^{n\cdot m}\\\\a^{-n}=\left(\frac{1}{a}\right)^n\\\\8^{-\frac{2}{3}}=\left(2^3\right)^{-\frac{2}{3}}=2^{3\times(-\frac{2}{3})}=2^{-2}=\left(\frac{1}{2}\right)^2=\frac{1}{2}\times\frac{1}{2}=\boxed{\frac{1}{4}}$