Question
$\Big(\frac{-1}{4}\Big)^{3}\times\Big(\frac{-1}{4}\Big)=\Big(\frac{-1}{4}\Big)^{11}$

Answer

$\Big(\frac{-1}{4}\Big)^{3}\times\Big(\frac{-1}{4}\Big)^{\text{x}}=\Big(\frac{-1}{4}\Big)^{11}$
Solution:
Let $\Big(\frac{-1}{4}\Big)^{3}\times\Big(\frac{-1}{4}\Big)=\Big(\frac{-1}{4}\Big)^{11}$
$\Rightarrow​​​​\Big(\frac{-1}{4}\Big)^{\text{x}}=\frac{\Big(\frac{-1}{4}\Big)^{11}}{\Big(\frac{-1}{4}\Big)^{3}}$
$\Rightarrow\Big(\frac{-1}{4}\Big)^{\text{x}}=\Big(\frac{-1}{4}\Big)^{\text{11-3}}$ $\big[\because\text{a}^{\text{m}}+\text{a}^{\text{n}}=\text{a}^{\text{m-n}}\text{m}>\text{n}\big]$
$\Rightarrow\Big(\frac{-1}{4}\Big)^{\text{x}}=\Big(\frac{-1}{4}\Big)^{8}$
Since, base are equal do, ny equating the power the pawers, we get
$\text{x}=8$
$\therefore\Big(-\frac{1}{4}\Big)^{3}\times\Big(-\frac{1}{4}\Big)^{8}=\Big(-\frac{1}{4}\Big)^{11}$

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