Question : If $\left (\sqrt{5} \right)^{7}\div \left (\sqrt{5} \right)^{5}=5^{p},$ then the value of $p$ is:
Option 1: $5$
Option 2: $2$
Option 3: $\frac{3}{2}$
Option 4: $1$
Answer (1)
20th Jan, 2024
Correct Answer: $1$
Solution :
Given: $\frac{(\sqrt{5})^7}{(\sqrt{5})^5} = 5^p$
$⇒(\sqrt{5})^{7 - 5} = 5^p$
$⇒(\sqrt{5})^2 = 5^p$
$⇒5^{\frac{1}{2}×2} = 5^{p}$
$⇒5^1=5^p$
Comparing both sides, we get,
$\therefore p=1$
Hence, the correct answer is $1$.
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