Answer
$\frac{64m^6}{9}$
Work Step by Step
We start with the given expression: $(3^2)^{-1}(4m^2)^3$
To raise a power to a power, we multiply the exponents: $(3^{-2})(4m^2)^3$
The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$. We use this rule to rewrite the expression: $\frac{(4m^2)^3}{3^2}=\frac{(4m^2)^3}{3\times3}=\frac{(4m^2)^3}{9}$.
Now, we will simplify the numerator. To raise a product to a power, we raise each factor to the power and multiply: $\frac{4^3(m^2)^3}{9}$
To raise a power to a power, we multiply the exponents: $\frac{4^3m^6}{9}$
We expand and simplify the constant power: $\frac{4\times4\times4m^6}{9}=\frac{64m^6}{9}$
