Find the values of $x$ in each of the following:$ \left(2^{3}\right)^{4}=\left(2^{2}\right)^{x} $

Given:

\( \left(2^{3}\right)^{4}=\left(2^{2}\right)^{x} \)

To do: 

We have to find the value of $x$.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

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

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$

Therefore,

$(2^{3})^{4}=(2^{2})^{x}$

$\Rightarrow 2^{3 \times 4}=2^{2 \times x}$

$\Rightarrow 2^{12}=2^{2 x}$

Comparing both sides, we get,

$12=2x$

$\Rightarrow x=\frac{12}{2}$

$\Rightarrow x=6$

The value of $x$ is $6$. 

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Updated on: 10-Oct-2022

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