Simplify ((x^5y^2)^2)/(x^-3y^7)

$\frac{{(x^{5} y^{2})}^{2}}{x^{- 3} y^{7}}$

Step 1

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

$\frac{{(x^{5} y^{2})}^{2} x^{3}}{y^{7}}$

Step 2

Simplify the numerator.

Apply the product rule to $x^{5} y^{2}$ .

$\frac{{(x^{5})}^{2} {(y^{2})}^{2} x^{3}}{y^{7}}$

Multiply the exponents in ${(x^{5})}^{2}$ .

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

$\frac{x^{5 \cdot 2} {(y^{2})}^{2} x^{3}}{y^{7}}$

Multiply $5$ by $2$ .

$\frac{x^{10} {(y^{2})}^{2} x^{3}}{y^{7}}$

Multiply the exponents in ${(y^{2})}^{2}$ .

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

$\frac{x^{10} y^{2 \cdot 2} x^{3}}{y^{7}}$

Multiply $2$ by $2$ .

$\frac{x^{10} y^{4} x^{3}}{y^{7}}$

Multiply $x^{10}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\frac{x^{3} x^{10} y^{4}}{y^{7}}$

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

$\frac{x^{3 + 10} y^{4}}{y^{7}}$

Add $3$ and $10$ .

$\frac{x^{13} y^{4}}{y^{7}}$

Step 3

Cancel the common factor of $y^{4}$ and $y^{7}$ .

Factor $y^{4}$ out of $x^{13} y^{4}$ .

$\frac{y^{4} x^{13}}{y^{7}}$

Cancel the common factors.

Factor $y^{4}$ out of $y^{7}$ .

$\frac{y^{4} x^{13}}{y^{4} y^{3}}$

Cancel the common factor.

$\frac{y^{4} x^{13}}{y^{4} y^{3}}$

Rewrite the expression.

$\frac{x^{13}}{y^{3}}$