Question : If $p=9, q=\sqrt{17}$, then the value of $(p^2-q^2)^{-\frac{1}{3}}$ is equal to:
Option 1: 4
Option 2: $\frac{1}{4}$
Option 3: 3
Option 4: $\frac{1}{3}$
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Correct Answer: $\frac{1}{4}$
Solution :
Given: $p=9⇒p^2 = 81$ and $q=\sqrt{17}⇒ q^2= 17$
Putting the values in the equation, we get,
$(p^2–q^2)^{–\frac{1}{3}}$
$=(81–17)^{–\frac{1}{3}}$
$=(64)^{–\frac{1}{3}}$
$=(4^3)^{–\frac{1}{3}}$
$=(4)^{–{1}}$
$=\frac{1}{4}$
Hence, the correct answer is $\frac{1}{4}$.
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