The value of frac{(81)^{3.6} times (9)^{2.7}} | vedclass

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Question

(C) Given expression $= \frac{(81)^{3.6} 	imes (9)^{2.7}}{(81)^{4.2} 	imes 3}$Expressing all terms with base $3$:$= \frac{(3^4)^{3.6} 	imes (3^2)^{

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(C) Given expression $= \frac{(81)^{3.6} 	imes (9)^{2.7}}{(81)^{4.2} 	imes 3}$Expressing all terms with base $3$:$= \frac{(3^4)^{3.6} 	imes (3^2)^{2.7}}{(3^4)^{4.2} 	imes 3^1}$Using the exponent rule $(a^m)^n = a^{m 	imes n}$:$= \frac{3^{14.4} 	imes 3^{5.4}}{3^{16.8} 	imes 3^1}$Using the rule $a^m 	imes a^n = a^{m+n}$:$= \frac{3^{14.4 + 5.4}}{3^{16.8 + 1}} = \frac{3^{19.8}}{3^{17.8}}$Using the rule $a^m \div a^n = a^{m-n}$:$= 3^{19.8 - 17.8} = 3^2 = 9$

The value of $\frac{(81)^{3.6} \times (9)^{2.7}}{(81)^{4.2} \times 3}$ is

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