Question

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

Answer 1

Answer:

$\textsf{B)} \quad \dfrac{1}{3^9 \cdot 6^{18}}$

Step-by-step explanation:

$(3^3 \cdot 6^6)^{-3}$

$\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:$

$\implies \dfrac{1}{(3^3 \cdot 6^6)^3}$

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

$\implies \dfrac{1}{(3^3)^3 \cdot (6^6)^3}$

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

$\implies \dfrac{1}{3^9 \cdot 6^{18}}$

Answer 2

$\\ \rm\Rrightarrow (3^3.6^6)^{-3}$

$\\ \rm\Rrightarrow \dfrac{1}{(3^36^6)^3}$

• (a^n)^m=a^mn

$\\ \rm\Rrightarrow \dfrac{1}{3^96^{18}}$

Option B