Simplify left(frac{1}{64}right)^{0}+(64)^{-1 | vedclass

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Question

(A) Given expression: $\left(\frac{1}{64}\right)^{0}+(64)^{-1 / 2}+(-32)^{4 / 5}$Step $1$: Any non-zero number raised to the power of $0$ is $1$. So,$

Vedclass · Accepted Answer

$17 \frac{1}{8}$

Vedclass · Answer

(A) Given expression: $\left(\frac{1}{64}ight)^{0}+(64)^{-1 / 2}+(-32)^{4 / 5}$Step $1$: Any non-zero number raised to the power of $0$ is $1$. So,$\left(\frac{1}{64}ight)^{0} = 1$.Step $2$: Evaluate $(64)^{-1/2}$. Since $64 = 8^2$,we have $(8^2)^{-1/2} = 8^{2 	imes (-1/2)} = 8^{-1} = \frac{1}{8}$.Step $3$: Evaluate $(-32)^{4/5}$. We know $32 = 2^5$. Thus,$(-32)^{4/5} = ((-1) 	imes 2^5)^{4/5} = (-1)^{4/5} 	imes (2^5)^{4/5}$. Since the exponent $4/5$ involves an even numerator and odd denominator,$(-1)^{4/5} = ((-1)^4)^{1/5} = 1^{1/5} = 1$. Then,$(2^5)^{4/5} = 2^{5 	imes 4/5} = 2^4 = 16$.Step $4$: Combine the results: $1 + \frac{1}{8} + 16 = 17 + \frac{1}{8} = 17 \frac{1}{8}$.

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

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