Math Snap

STEP 1

Assumptions1. The expression to be simplified is $\left(\frac{3 a}{b^{-3}}\right)^{3}$.
. The exponent rule states that $(a^m)^n = a^{mn}$.
3. The exponent rule also states that $a^{-n} = \frac{1}{a^n}$.

STEP 2

First, we will apply the exponent rule to the expression. This rule states that $(a^m)^n = a^{mn}$.
$$\left(\frac{ a}{b^{-}}\right)^{} = \left(^ a^\right) / \left(b^{-*}\right)
$$

STEP 3

Now, calculate the values of $3^3$ and $-3*3$.
$$\left(\frac{3 a}{b^{-3}}\right)^{3} = \left(27 a^3\right) / \left(b^{-9}\right)
$$

STEP 4

Next, we will apply the exponent rule that states $a^{-n} = \frac{1}{a^n}$ to $b^{-9}$.
$$\left(\frac{3 a}{b^{-3}}\right)^{3} = \left(27 a^3\right) / \left(\frac{1}{b^9}\right)
$$

Now, simplify the expression by multiplying the numerator and denominator by $b^9$.
$$\left(\frac{3 a}{b^{-3}}\right)^{3} =27 a^3 b^9$$The simplified expression with only positive exponents is $27 a^3 b^9$.