Simplify x^3(y^-5)(x^-8)

$x^{3} (y^{- 5}) (x^{- 8})$

Step 1

Multiply $x^{3}$ by $x^{- 8}$ by adding the exponents.

Move $x^{- 8}$ .

$x^{- 8} x^{3} y^{- 5}$

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

$x^{- 8 + 3} y^{- 5}$

Add $- 8$ and $3$ .

$x^{- 5} y^{- 5}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 4

Combine.

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

Step 5

Multiply $1$ by $1$ .

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