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The value of \( x \) for which \( \left(\frac{7}{8}\right)^{-4} \times\left(\frac{7}{8}\right)^{3 x}=\left(\frac{7}{8}\right)^{8} \), is equal to
Given:
$(\frac{7}{8})^{-4} \times(\frac{7}{8})^{3 x}=(\frac{7}{8})^{8}$.
To do:
We have to find the value of $x$.
Solution:
We know that,
$a^m \times a^n=a^{m+n}$
Therefore,
LHS
$(\frac{7}{8})^{-4} \times(\frac{7}{8})^{3 x}=(\frac{7}{8})^{-4+3x}$
$=(\frac{7}{8})^{3x-4}$
RHS $=(\frac{7}{8})^{8}$
On comparing LHS and RHS,
$3x-4=8$
$3x=8+4$
$x=\frac{12}{3}$
$x=4$
The value of $x$ is $4$.
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