Find the value of 625^{frac{3}{4}}. | vedclass

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Question

(A) To find the value of $625^{\frac{3}{4}}$,we first express $625$ as a power of $5$.Since $5 	imes 5 	imes 5 	imes 5 = 625$,we can write $625 = 5

Vedclass · Accepted Answer

$125$

Vedclass · Answer

(A) To find the value of $625^{\frac{3}{4}}$,we first express $625$ as a power of $5$.Since $5 	imes 5 	imes 5 	imes 5 = 625$,we can write $625 = 5^{4}$.Now,substitute this into the expression: $625^{\frac{3}{4}} = (5^{4})^{\frac{3}{4}}$.Using the power of a power rule $(a^{m})^{n} = a^{m 	imes n}$,we get $5^{4 	imes \frac{3}{4}}$.Simplifying the exponent,$4 	imes \frac{3}{4} = 3$.Therefore,the expression becomes $5^{3}$.Calculating $5^{3} = 5 	imes 5 	imes 5 = 125$.

Find the value of $625^{\frac{3}{4}}$.

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