Question

Simplify the following using laws of indices:
$(16{)}^{-0.75}\times (64{)}^{4/3}$

Answer 1

Given, $(16{)}^{-0.75}\times (64{)}^{4/3}$

$=$ $(2^4{)}^{-3/4}\times (4^3{)}^{4/3}$

$=$ $\left(2^{-3}\right)\times (4{)}^4$ Using $\left[\right(A^m{)}^n=A^{mn}]$

$=$ $\left(2^{-3}\right)\times (2^2{)}^4$

$=$ $2^{-3}\times 2^8$ Using $\left[\right(A^m{)}^n=A^{mn}]$

$=$ $2^{-3+8}$

$=$ $2^5$

$=$ $32$