Evaluate (x^-8y^-6)/(x^7y^4)

$\frac{x^{- 8} y^{- 6}}{x^{7} y^{4}}$

Step 1

Move $x^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{y^{- 6}}{x^{7} y^{4} x^{8}}$

Step 2

Move $y^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{7} y^{4} x^{8} y^{6}}$

Step 3

Simplify the denominator.

Multiply $x^{7}$ by $x^{8}$ by adding the exponents.

Move $x^{8}$ .

$\frac{1}{x^{8} x^{7} y^{4} y^{6}}$

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

$\frac{1}{x^{8 + 7} y^{4} y^{6}}$

Add $8$ and $7$ .

$\frac{1}{x^{15} y^{4} y^{6}}$

Multiply $y^{4}$ by $y^{6}$ by adding the exponents.

Move $y^{6}$ .

$\frac{1}{x^{15} (y^{6} y^{4})}$

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

$\frac{1}{x^{15} y^{6 + 4}}$

Add $6$ and $4$ .

$\frac{1}{x^{15} y^{10}}$