Simplify (24x^4y)/(3x^-4y^-1)

$\frac{24 x^{4} y}{3 x^{- 4} y^{- 1}}$

Step 1

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

$\frac{24 x^{4} y x^{4}}{3 y^{- 1}}$

Step 2

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

$\frac{24 x^{4} y x^{4} y}{3}$

Step 3

Simplify the numerator.

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

Move $x^{4}$ .

$\frac{24 (x^{4} x^{4}) y \cdot y}{3}$

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

$\frac{24 x^{4 + 4} y \cdot y}{3}$

Add $4$ and $4$ .

$\frac{24 x^{8} y \cdot y}{3}$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$\frac{24 x^{8} (y \cdot y)}{3}$

Multiply $y$ by $y$ .

$\frac{24 x^{8} y^{2}}{3}$

Step 4

Cancel the common factor of $24$ and $3$ .

Factor $3$ out of $24 x^{8} y^{2}$ .

$\frac{3 (8 x^{8} y^{2})}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (8 x^{8} y^{2})}{3 (1)}$

Cancel the common factor.

$\frac{3 (8 x^{8} y^{2})}{3 \cdot 1}$

Rewrite the expression.

$\frac{8 x^{8} y^{2}}{1}$

Divide $8 x^{8} y^{2}$ by $1$ .

$8 x^{8} y^{2}$