Question

Simplify the following using laws of indices:
$(6.25{)}^{0.5}\times {10}^2\times (100{)}^{-1/2}$

Answer 1

Given, $(6.25{)}^{0.5}\times {10}^2\times (100{)}^{-1/2}$

$=$ $(6.25{)}^{0.5}\times {10}^2\times ({10}^2{)}^{-1/2}$

$=$ $(6.25{)}^{0.5}\times {10}^2\times (10{)}^{-1}$ Using $\left[\right(A^m{)}^n=A^{mn}]$

$=$ $(6.25{)}^{0.5}\times {10}^1$ Using $[A^m\times A^n=A^{m+n}]$

$=$ $\left(\right(2.5{)}^2{)}^{0.5}\times {10}^1$

$=$ $(2.5{)}^1\times {10}^1$ Using $\left[\right(A^m{)}^n=A^{mn}]$

$=$ $2.5\times 10$

$=$ $25$