Simplify ((24x^-3)/(12x^-2))^2

${(\frac{24 x^{- 3}}{12 x^{- 2}})}^{2}$

Step 1

Move $x^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{24}{12 x^{- 2} x^{3}})}^{2}$

Step 2

Simplify the denominator.

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

Move $x^{3}$ .

${(\frac{24}{12 (x^{3} x^{- 2})})}^{2}$

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

${(\frac{24}{12 x^{3 - 2}})}^{2}$

Subtract $2$ from $3$ .

${(\frac{24}{12 x^{1}})}^{2}$

Simplify $12 x^{1}$ .

${(\frac{24}{12 x})}^{2}$

Step 3

Cancel the common factor of $24$ and $12$ .

Factor $12$ out of $24$ .

${(\frac{12 \cdot 2}{12 x})}^{2}$

Cancel the common factors.

Factor $12$ out of $12 x$ .

${(\frac{12 \cdot 2}{12 (x)})}^{2}$

Cancel the common factor.

${(\frac{12 \cdot 2}{12 x})}^{2}$

Rewrite the expression.

${(\frac{2}{x})}^{2}$

Step 4

Simplify the expression.

Apply the product rule to $\frac{2}{x}$ .

$\frac{2^{2}}{x^{2}}$

Raise $2$ to the power of $2$ .

$\frac{4}{x^{2}}$