Question

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

Answer 1

`\\ \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)`

Answer 2

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)`