Answer
-3
Work Step by Step
You are given ($m^{2}$$n^{3}$$)^{?}$=$\frac{1}{m^6n^9}$.Solve for the blank:
($m^{2}$$)^{?}$ ($n^{3}$$)^{?}$=$\frac{1}{m^6n^9}$ -multiply each term outside the term to the power ?-
$m^{2?}$$n^{3?}$=$\frac{1}{m^6n^9}$ -use power to power rule-
$\frac{1}{m^6}$=$m^{-6}$ and $\frac{1}{n^9}$=$n^{-9}$ -apply exponent rule $\frac{1}{a^b}$=$a^{-b}$-
2?=-6 and 3?=-9 -we need to have common base exponents
which equal each other-
?=-3 -isolate the blank-
=($m^{2}$$n^{3}$$)^{-3}$=$\frac{1}{m^6n^9}$
