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Maths-

General

Easy

Question

Which of the following is an equivalent form of $cube root of straight f to the power of 6 straight a end exponent space straight k squared end root$ , where f > 0 and k > 0 ?

$f^{\frac{1}{3 a}} k^{- 1}$
$f^{\frac{1}{2 a}} k^{\frac{3}{2}}$
$f^{3 a} k^{- 1}$
$f^{2 a} k^{\frac{2}{3}}$

The correct answer is: $straight f to the power of 2 straight a end exponent space straight k to the power of 2 over 3 end exponent$

HINT: Rewrite the given expression and then get the equivalent form.
Complete step by step solution:
Given $cube root of straight f to the power of 6 straight a end exponent space straight k squared end root$
This can be written as, $open parentheses straight f to the power of 6 straight a end exponent space straight k squared close parentheses space to the power of fraction numerator 1 over denominator 3 space end fraction end exponent equals space straight f to the power of fraction numerator 6 straight a over denominator 3 end fraction end exponent space cross times space straight k to the power of 2 over 3 end exponent$
On simplification, we get it as $straight f to the power of 2 straight a end exponent space cross times space straight k to the power of 2 over 3 end exponent$
Hence option D is the answer

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