Find the value of n:$4^{2n} \times 4^n = 2^{12}$

Given :

The given expression is $4^{2n} \times 4^n = 2^{12}$.

To do :

We have to find the value of n.

Solution :

$4^{2n} \times 4^n = 2^{12}$

We know that,

$a^m \times a^n= a^{m+n}$

$2^{12}$ can be written as,

$2^{12}= (2^2)^6 = 4^6$

$4^{2n}\times 4^n = 2^{12}$

$4^{2n}\times 4^n =4^6$

$(4)^{2n+n}= 4^6$

Comparing the powers on both sides, we get,

$2n+n = 6$

$3n = 6$

$n = \frac{6}{3}$

$n = 2$.

The value of n is 2.

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Updated on: 10-Oct-2022

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