Simplify (15x^5y^-2)/(3x^7y^-3)

$\frac{15 x^{5} y^{- 2}}{3 x^{7} y^{- 3}}$

Step 1

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

$\frac{15 x^{5} y^{- 2} y^{3}}{3 x^{7}}$

Step 2

Simplify the numerator.

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

Move $y^{3}$ .

$\frac{15 x^{5} (y^{3} y^{- 2})}{3 x^{7}}$

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

$\frac{15 x^{5} y^{3 - 2}}{3 x^{7}}$

Subtract $2$ from $3$ .

$\frac{15 x^{5} y^{1}}{3 x^{7}}$

Simplify $15 x^{5} y^{1}$ .

$\frac{15 x^{5} y}{3 x^{7}}$

Step 3

Cancel the common factor of $15$ and $3$ .

Factor $3$ out of $15 x^{5} y$ .

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

Cancel the common factors.

Factor $3$ out of $3 x^{7}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{5 x^{5} y}{x^{7}}$

Step 4

Cancel the common factor of $x^{5}$ and $x^{7}$ .

Factor $x^{5}$ out of $5 x^{5} y$ .

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

Cancel the common factors.

Factor $x^{5}$ out of $x^{7}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{5 y}{x^{2}}$