Question

Select the equivalent expression (3^3*6^6)^-3

Answer 1

`\\ \rm\Rrightarrow (3^3.6^6)^(-3)`

`\\ \rm\Rrightarrow (1)/((3^36^6)^3)`

• (a^n)^m=a^mn

`\\ \rm\Rrightarrow (1)/(3^96^(18))`

Option B

Answer 2

`\textsf{B)} \quad (1)/(3^9 \cdot 6^(18))`

Explanation:

`(3^3 \cdot 6^6)^(-3)`

`\textsf{Apply exponent rule} \quad a^(-n)=(1)/(a^n):`

`\implies (1)/((3^3 \cdot 6^6)^3)`

`\textsf{Apply exponent rule} \quad (ab)^c=a^c \cdot b^c:`

`\implies (1)/((3^3)^3 \cdot (6^6)^3)`

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

`\implies (1)/(3^9 \cdot 6^(18))`