Simplify (x^2y^-7)/(x^8y^-5)

$\frac{x^{2} y^{- 7}}{x^{8} y^{- 5}}$

Step 1

Move $y^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x^{2}}{x^{8} y^{- 5} y^{7}}$

Step 2

Multiply $y^{- 5}$ by $y^{7}$ by adding the exponents.

Move $y^{7}$ .

$\frac{x^{2}}{x^{8} (y^{7} y^{- 5})}$

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

$\frac{x^{2}}{x^{8} y^{7 - 5}}$

Subtract $5$ from $7$ .

$\frac{x^{2}}{x^{8} y^{2}}$

Step 3

Cancel the common factor of $x^{2}$ and $x^{8}$ .

Multiply by $1$ .

$\frac{x^{2} \cdot 1}{x^{8} y^{2}}$

Cancel the common factors.

Factor $x^{2}$ out of $x^{8} y^{2}$ .

$\frac{x^{2} \cdot 1}{x^{2} (x^{6} y^{2})}$

Cancel the common factor.

$\frac{x^{2} \cdot 1}{x^{2} (x^{6} y^{2})}$

Rewrite the expression.

$\frac{1}{x^{6} y^{2}}$