which is the simplified form of the expression $\frac{(6^{-4})^{-9}}{6^{6}}$?\n$\frac{1}{6^{42}}$\n$\frac{1}{…

which is the simplified form of the expression $\frac{(6^{-4})^{-9}}{6^{6}}$?\n$\frac{1}{6^{42}}$\n$\frac{1}{6^{19}}$\n$6^{6}$\n$6^{30}$

Answer

Use the power - of - a - power rule $(a^m)^n=a^{mn}$. For $(6^{-4})^{-9}$, we have $(-4)\times(-9) = 36$, so $(6^{-4})^{-9}=6^{36}$.

The quotient rule is $\frac{a^m}{a^n}=a^{m - n}$. Here, $a = 6$, $m = 36$, and $n = 6$. So $\frac{6^{36}}{6^{6}}=6^{36 - 6}$.

$36-6 = 30$, so $\frac{6^{36}}{6^{6}}=6^{30}$.

$6^{30}$