find the value of n. 2^n 2^6 2^ -3 =2^ 18 - Vidyadip

Question

find the value of n. $\frac{2^\text{n}\times2^6}{2^{-3}}=2^{18}$

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Answer

Given,
$\frac{2^\text{n}\times2^6}{2^{-3}}=2^{18}$
Using law of exponents, $\text{a}^{-\text{m}}=\frac{1}{\text{a}^{\text{m}}}$ [$\because$ a is non-zero integer]
$\Rightarrow2^\text{n}\times2^6\times2^3=2^{18}$
$\Rightarrow2^{\text{n}+9}=2^{18}$ $\left[\because a^m \times a^n=a^{m+n}\right]$
On camparing both side, we get
$n + 9 = 18 \left[\because a^m \div a^n=a^{m+n}\right]$
$ ⇒ n = 9$

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