Question

Question 119

Find the value of n.
$\frac{2^n\times 2^6}{2^{-3}}=2^{18}$

Answer 1

Given, $\frac{2^n\times 2^6}{2^{-3}}=2^{18}$
Using the law of exponents,
$a^{-m}=\frac{1}{a^m},$
we get,

$\frac{2^n\times 2^6}{2^{-3}}=2^{18}$

$\Rightarrow 2^n\times 2^6\times 2^3=2^{18}$

$\Rightarrow 2^{n+6+3}=2^{18}$
$\Rightarrow 2^{n+9}=2^{18}$

Since the base is same on both sides, we can equate the exponents.
$\Rightarrow n+9=18\Rightarrow n=18-9\Rightarrow n=9$