Evaluate (x^7x^-3y)/(y^-2)

$\frac{x^{7} x^{- 3} y}{y^{- 2}}$

Step 1

Multiply $x^{7}$ by $x^{- 3}$ by adding the exponents.

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

$\frac{x^{7 - 3} y}{y^{- 2}}$

Subtract $3$ from $7$ .

$\frac{x^{4} y}{y^{- 2}}$

Step 2

Move $y^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$x^{4} y \cdot y^{2}$

Step 3

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

Move $y^{2}$ .

$x^{4} (y^{2} y)$

Multiply $y^{2}$ by $y$ .

Raise $y$ to the power of $1$ .

$x^{4} (y^{2} y^{1})$

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

$x^{4} y^{2 + 1}$

Add $2$ and $1$ .

$x^{4} y^{3}$