The value of ≤ft(1/64)^{0}+(64)^{-1/2}+(-32)^{4/5}

Correct Answer is : 1718171/81781

Correct Answer is : 1718171/81781

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Question : 56 of 86

Marks: +1, -0

The value of

\left(\frac{1}{64}\right)^{0}+(64)^{-\frac{1}{2}}+(-32)^{\frac{4}{5}}

Solution:

Concept:

Use laws of indices: any nonzero number to power 0 is 1, negative exponent means reciprocal, and rational exponent means root and power.

Explanation:

First term:

\left(\frac{1}{64}\right)^0 = 1

(since any nonzero number raised to 0 is 1).

Second term:

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

Third term:

(-32)^{\frac{4}{5}} = [(-32)^{\frac{1}{5}}]^4

. The fifth root of

-32

-2

because

(-2)^5 = -32

. Then

(-2)^4 = 16

Sum:

1 + \frac{1}{8} + 16 = 17\frac{1}{8}

Answer:

17\frac{1}{8}

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