The value of frac{9^{2} times 18^{4}}{3^{16}} | vedclass

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Question

(C) Given expression is $\frac{9^{2} 	imes 18^{4}}{3^{16}}$.Expressing the bases in terms of prime factors:$9 = 3^{2}$ and $18 = 2 	imes 3^{2}$.Subs

Vedclass · Accepted Answer

$\frac{16}{81}$

Vedclass · Answer

(C) Given expression is $\frac{9^{2} 	imes 18^{4}}{3^{16}}$.Expressing the bases in terms of prime factors:$9 = 3^{2}$ and $18 = 2 	imes 3^{2}$.Substituting these into the expression:$= \frac{(3^{2})^{2} 	imes (2 	imes 3^{2})^{4}}{3^{16}}$$= \frac{3^{4} 	imes 2^{4} 	imes (3^{2})^{4}}{3^{16}}$$= \frac{3^{4} 	imes 2^{4} 	imes 3^{8}}{3^{16}}$$= \frac{3^{4+8} 	imes 2^{4}}{3^{16}}$$= \frac{3^{12} 	imes 2^{4}}{3^{16}}$$= \frac{2^{4}}{3^{16-12}}$$= \frac{16}{3^{4}}$$= \frac{16}{81}$.

The value of $\frac{9^{2} \times 18^{4}}{3^{16}}$ is

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