Evaluate (2x^4y^-4)/(8x^7y^3)

$\frac{2 x^{4} y^{- 4}}{8 x^{7} y^{3}}$

Step 1

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

$\frac{2 x^{4}}{8 x^{7} y^{3} y^{4}}$

Step 2

Multiply $y^{3}$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$\frac{2 x^{4}}{8 x^{7} (y^{4} y^{3})}$

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

$\frac{2 x^{4}}{8 x^{7} y^{4 + 3}}$

Add $4$ and $3$ .

$\frac{2 x^{4}}{8 x^{7} y^{7}}$

Step 3

Cancel the common factor of $2$ and $8$ .

Factor $2$ out of $2 x^{4}$ .

$\frac{2 (x^{4})}{8 x^{7} y^{7}}$

Cancel the common factors.

Factor $2$ out of $8 x^{7} y^{7}$ .

$\frac{2 (x^{4})}{2 (4 x^{7} y^{7})}$

Cancel the common factor.

$\frac{2 x^{4}}{2 (4 x^{7} y^{7})}$

Rewrite the expression.

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

Step 4

Cancel the common factor of $x^{4}$ and $x^{7}$ .

Multiply by $1$ .

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

Cancel the common factors.

Factor $x^{4}$ out of $4 x^{7} y^{7}$ .

$\frac{x^{4} \cdot 1}{x^{4} (4 x^{3} y^{7})}$

Cancel the common factor.

$\frac{x^{4} \cdot 1}{x^{4} (4 x^{3} y^{7})}$

Rewrite the expression.

$\frac{1}{4 x^{3} y^{7}}$