Evaluate (x^-4)/(x^8*x^-1)

$\frac{x^{- 4}}{x^{8} \cdot x^{- 1}}$

Step 1

Multiply $x^{8}$ by $x^{- 1}$ by adding the exponents.

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

$\frac{x^{- 4}}{x^{8 - 1}}$

Subtract $1$ from $8$ .

$\frac{x^{- 4}}{x^{7}}$

Step 2

Move $x^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{7} x^{4}}$

Step 3

Multiply $x^{7}$ by $x^{4}$ by adding the exponents.

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

$\frac{1}{x^{7 + 4}}$

Add $7$ and $4$ .

$\frac{1}{x^{11}}$