Simplify (x^-4y^6y^3)/(x^-7)

$\frac{x^{- 4} y^{6} y^{3}}{x^{- 7}}$

Step 1

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

Move $y^{3}$ .

$\frac{x^{- 4} (y^{3} y^{6})}{x^{- 7}}$

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

$\frac{x^{- 4} y^{3 + 6}}{x^{- 7}}$

Add $3$ and $6$ .

$\frac{x^{- 4} y^{9}}{x^{- 7}}$

Step 2

Move $x^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$x^{- 4} y^{9} x^{7}$

Step 3

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

Move $x^{7}$ .

$x^{7} x^{- 4} y^{9}$

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

$x^{7 - 4} y^{9}$

Subtract $4$ from $7$ .

$x^{3} y^{9}$