16 10^2 64 2^4 4^2 - Vidyadip

Question

$\frac{16\times10^2\times64}{2^4\times4^2}$

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Answer

Using laws of exponents, $a^m÷ a^n= (a)^{m-n} $ and $a^m× a^n= a^{m+n}$ [$\because$ a is non-zero integer]
$\therefore$ $\frac{16\times10^2\times64}{2^4\times4^2}$
$ =(4)^2 \times 10^2 \times 2^{-4} \times(4)^3 \times 4^{-2}[\because 64=4 \times 4 \times 4 \text { and } 16=4 \times 4] $
$ =\left(2^2\right)^3 \times 10^2 \times 2^{-4} $
$ =2^6 \times 10^2 \times 2^{-4} $
$ =2^2 \times 10^2 $
$ =4 \times 100\left[\because 2^2=4\right] $
$= 400$

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