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

Question 1

Question 2

$\\ \rm\Rrightarrow ((11^6.6^9)^2)/(11^3)$

$\\ \rm\Rrightarrow (11^(6(2)).6^(9(2)))/(11^3)$

$\\ \rm\Rrightarrow (11^(12).6^(18))/(11^3)$

$\\ \rm\Rrightarrow \frac{11^(12-3)6^(18)}{}$

$\\ \rm\Rrightarrow 11^96^(18)$

Question 3

Answer:

B

Explanation:

$\sf Given \: expression\: :((11^6 \cdot 6^9)^2)/(11^3)$

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

$\sf \implies (11^(6 * 2) \cdot 6^(9*2))/(11^3)$

$\sf \implies (11^(12) \cdot 6^(18))/(11^3)$

$\sf \implies (11^(12))/(11^3) \cdot 6^(18)$

$\sf Apply\:exponent\:rule\quad (a^b)/(a^c)=a^(b-c) :$

$\sf \implies 11^(12-3) \cdot 6^(18)$

$\sf \implies 11^(9) \cdot 6^(18)$

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