Question

Simplify: $(64{)}^{-\frac{1}{3}}\times [(64{)}^{\frac{2}{3}}-(64{)}^{\frac{1}{3}}]$

• A. 3

Answer 1

The correct option is A 3
$(64{)}^{-\frac{1}{3}}\times [(64{)}^{\frac{2}{3}}-(64{)}^{\frac{1}{3}}]$
$=(4^3{)}^{-\frac{1}{3}}\times [(4^3{)}^{\frac{2}{3}}-(4^3{)}^{\frac{1}{3}}]$
$=(4{)}^{3\times (-\frac{1}{3})}\times [(4{)}^{3\times \frac{2}{3}}-(4{)}^{3\times \frac{1}{3}}]$
$(\because (a^m{)}^n=a^{m\times n})$
$=4^{-1}\times [4^2-4^1]$
$=4^{-1}\times [16-4]$
$=4^{-1}\times 12$
$=\frac{1}{4}\times 12(\because a^{-m}=\frac{1}{a^m})$
$=\frac{12}{4}=3$
Hence, the answer is 3.