Question

please prove both sides.​

Answer 1

$\textbf{Given:-} \: \frac{25 \times {2x}^{ - 4} }{ {5}^{ - 2} \times 10 {x}^{ - 6} } = {125x}^{2}$

$\textbf{To Prove:-} \: \frac{25 \times {2x}^{ - 4} }{ {5}^{ - 2} \times 10 {x}^{ - 6} } = {125x}^{2}$

Solution:-

$⇒\text{L.H.S} = \frac{25 \times {2x}^{ - 4} }{ {5}^{ - 2} \times 10 \times {x}^{ - 6} } \: \: \: \[ \left[ {a}^{ - 1} = \frac{1}{a} \right] \]$

$⇒ \frac{25 \times 2 {x}^{ - 4} + 6}{ {5}^{ - 2} \times 5 \times 2}$

$⇒ \frac{ {5}^{2} \times {x}^{2} }{ {5}^{ - 1} }$

$⇒ {5}^{2 + 1} \times {x}^{2}$

$⇒125 {x}^{2}$

$⇒\text{R.H.S}$

$\textbf{Hence,} \: \frac{25 \times {2x}^{ - 4} }{ {5}^{ - 2} \times 10 {x}^{ - 6} } = {125x}^{2}$

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Answer 2

Step-by-step explanation:

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