Question

Which expression is equivalent to ? Prove your choice is correct.

Answer 1

$\\ \rm\Rrightarrow \dfrac{(11^6.6^9)^2}{11^3}$

$\\ \rm\Rrightarrow \dfrac{11^{6(2)}.6^{9(2)}}{11^3}$

$\\ \rm\Rrightarrow \dfrac{11^{12}.6^{18}}{11^3}$

$\\ \rm\Rrightarrow \dfrac{11^{12-3}6^{18}}{}$

$\\ \rm\Rrightarrow 11^96^{18}$

Answer 2

Answer:

B

Step-by-step explanation:

$\sf Given \: expression\: :\dfrac{(11^6 \cdot 6^9)^2}{11^3}$

$\sf Apply\:exponent\:rule\quad (a^b)^c=a^{bc} :$

$\sf \implies \dfrac{11^{6 \times 2} \cdot 6^{9\times2}}{11^3}$

$\sf \implies \dfrac{11^{12} \cdot 6^{18}}{11^3}$

$\sf \implies \dfrac{11^{12}}{11^3} \cdot 6^{18}$

$\sf Apply\:exponent\:rule\quad \dfrac{a^b}{a^c}=a^{b-c} :$

$\sf \implies 11^{12-3} \cdot 6^{18}$

$\sf \implies 11^{9} \cdot 6^{18}$