Simplify : frac{(25)^{frac{3}{2}} times (243) | vedclass

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Question

(B) Given expression: $\frac{(25)^{\frac{3}{2}} 	imes (243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}} 	imes (8)^{\frac{4}{3}}}$Step $1$: Express each base a

Vedclass · Accepted Answer

$3375/512$

Vedclass · Answer

(B) Given expression: $\frac{(25)^{\frac{3}{2}} 	imes (243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}} 	imes (8)^{\frac{4}{3}}}$Step $1$: Express each base as a power of its prime factors.$25 = 5^2$,$243 = 3^5$,$16 = 2^4$,$8 = 2^3$.Step $2$: Substitute these into the expression:$= \frac{(5^2)^{\frac{3}{2}} 	imes (3^5)^{\frac{3}{5}}}{(2^4)^{\frac{5}{4}} 	imes (2^3)^{\frac{4}{3}}}$Step $3$: Apply the power rule $(a^m)^n = a^{m 	imes n}$:$= \frac{5^{2 	imes \frac{3}{2}} 	imes 3^{5 	imes \frac{3}{5}}}{2^{4 	imes \frac{5}{4}} 	imes 2^{3 	imes \frac{4}{3}}}$$= \frac{5^3 	imes 3^3}{2^5 	imes 2^4}$Step $4$: Simplify the powers:$= \frac{125 	imes 27}{2^{5+4}}$$= \frac{3375}{2^9}$$= \frac{3375}{512}$

Simplify $: \frac{(25)^{\frac{3}{2}} \times (243)^{\frac{3}{5}}}{(16)^{\frac{5}{4}} \times (8)^{\frac{4}{3}}}$

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