64^{-\;1/2}-(-32)^{-\;4/5}= x, then the value of x is

Correct Answer is : 316\;3/16163

Correct Answer is : 316\;3/16163

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Question : 7 of 86

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64^{-\;\frac{1}{2}}-(-32)^{-\;\frac{4}{5}}= x,

x

Solution:

Concept:

Simplify each term using laws of indices:

a^{-m} = \frac{1}{a^m}

and for a negative base with odd root, the real value is defined.

Explanation:

First term:

64^{-1/2} = \frac{1}{64^{1/2}} = \frac{1}{\sqrt{64}} = \frac{1}{8}

Second term:

(-32)^{-4/5}

. Since the denominator of the exponent is 5 (odd),

(-32)^{1/5} = -2

. Then

(-32)^{4/5} = [(-32)^{1/5}]^4 = (-2)^4 = 16

. Hence

(-32)^{-4/5} = \frac{1}{16}

Now

x = \frac{1}{8} - \frac{1}{16} = \frac{2}{16} - \frac{1}{16} = \frac{1}{16}

Answer:

x = \frac{1}{16}

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