Simplify (x^-6)/(x^3y^8y^2)

$\frac{x^{- 6}}{x^{3} y^{8} y^{2}}$

Step 1

Multiply $y^{8}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$\frac{x^{- 6}}{x^{3} (y^{2} y^{8})}$

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

$\frac{x^{- 6}}{x^{3} y^{2 + 8}}$

Add $2$ and $8$ .

$\frac{x^{- 6}}{x^{3} y^{10}}$

Step 2

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

$\frac{1}{x^{3} y^{10} x^{6}}$

Step 3

Multiply $x^{3}$ by $x^{6}$ by adding the exponents.

Move $x^{6}$ .

$\frac{1}{x^{6} x^{3} y^{10}}$

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

$\frac{1}{x^{6 + 3} y^{10}}$

Add $6$ and $3$ .

$\frac{1}{x^{9} y^{10}}$