The value of (256)^{0.16} times (256)^{0.09} | vedclass

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Question

(A) Using the law of exponents,$a^m 	imes a^n = a^{m+n}$.Given expression: $(256)^{0.16} 	imes (256)^{0.09} = (256)^{0.16 + 0.09}$.Adding the expone

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) Using the law of exponents,$a^m 	imes a^n = a^{m+n}$.Given expression: $(256)^{0.16} 	imes (256)^{0.09} = (256)^{0.16 + 0.09}$.Adding the exponents: $(256)^{0.25}$.Since $0.25 = \frac{1}{4}$,we have $(256)^{\frac{1}{4}}$.Expressing $256$ as a power of $4$: $256 = 4^4$.Therefore,$(4^4)^{\frac{1}{4}} = 4^{4 	imes \frac{1}{4}} = 4^1 = 4$.Hence,the correct option is $A$.

The value of $(256)^{0.16} \times (256)^{0.09}$ is

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