Evaluate (x^-6x^5y^3)/(y^8)

$\frac{x^{- 6} x^{5} y^{3}}{y^{8}}$

Step 1

Multiply $x^{- 6}$ by $x^{5}$ by adding the exponents.

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

$\frac{x^{- 6 + 5} y^{3}}{y^{8}}$

Add $- 6$ and $5$ .

$\frac{x^{- 1} y^{3}}{y^{8}}$

Step 2

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

$\frac{y^{3}}{y^{8} x}$

Step 3

Cancel the common factor of $y^{3}$ and $y^{8}$ .

Multiply by $1$ .

$\frac{y^{3} \cdot 1}{y^{8} x}$

Cancel the common factors.

Factor $y^{3}$ out of $y^{8} x$ .

$\frac{y^{3} \cdot 1}{y^{3} (y^{5} x)}$

Cancel the common factor.

$\frac{y^{3} \cdot 1}{y^{3} (y^{5} x)}$

Rewrite the expression.

$\frac{1}{y^{5} x}$