Simplify (24x^4y^-2)/((2xy)^2)

$\frac{24 x^{4} y^{- 2}}{{(2 x y)}^{2}}$

Step 1

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

$\frac{24 x^{4}}{{(2 x y)}^{2} y^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $2 x y$ .

$\frac{24 x^{4}}{{(2 x)}^{2} y^{2} y^{2}}$

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$\frac{24 x^{4}}{{(2 x)}^{2} (y^{2} y^{2})}$

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

$\frac{24 x^{4}}{{(2 x)}^{2} y^{2 + 2}}$

Add $2$ and $2$ .

$\frac{24 x^{4}}{{(2 x)}^{2} y^{4}}$

Apply the product rule to $2 x$ .

$\frac{24 x^{4}}{2^{2} x^{2} y^{4}}$

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

$\frac{24 x^{4}}{4 x^{2} y^{4}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $24$ and $4$ .

Factor $4$ out of $24 x^{4}$ .

$\frac{4 (6 x^{4})}{4 x^{2} y^{4}}$

Cancel the common factors.

Factor $4$ out of $4 x^{2} y^{4}$ .

$\frac{4 (6 x^{4})}{4 (x^{2} y^{4})}$

Cancel the common factor.

$\frac{4 (6 x^{4})}{4 (x^{2} y^{4})}$

Rewrite the expression.

$\frac{6 x^{4}}{x^{2} y^{4}}$

Cancel the common factor of $x^{4}$ and $x^{2}$ .

Factor $x^{2}$ out of $6 x^{4}$ .

$\frac{x^{2} (6 x^{2})}{x^{2} y^{4}}$

Cancel the common factors.

Factor $x^{2}$ out of $x^{2} y^{4}$ .

$\frac{x^{2} (6 x^{2})}{x^{2} (y^{4})}$

Cancel the common factor.

$\frac{x^{2} (6 x^{2})}{x^{2} y^{4}}$

Rewrite the expression.

$\frac{6 x^{2}}{y^{4}}$