Simplify ((3x^3y^0)/(x^-2))^4

${(\frac{3 x^{3} y^{0}}{x^{- 2}})}^{4}$

Move $x^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(3 x^{3} y^{0} x^{2})}^{4}$

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

${(3 (x^{2} x^{3}) y^{0})}^{4}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(3 x^{2 + 3} y^{0})}^{4}$

Add $2$ and $3$ .

${(3 x^{5} y^{0})}^{4}$

Simplify $3 x^{5} y^{0}$ .

${(3 x^{5})}^{4}$

Apply the product rule to $3 x^{5}$ .

$3^{4} {(x^{5})}^{4}$

Raise $3$ to the power of $4$ .

$81 {(x^{5})}^{4}$

Multiply the exponents in ${(x^{5})}^{4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$81 x^{5 \cdot 4}$

Multiply $5$ by $4$ .

$81 x^{20}$