Simplify (4x^7y^-1)/((5y)^2-7y^2)

$\frac{4 x^{7} y^{- 1}}{{(5 y)}^{2} - 7 y^{2}}$

Step 1

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

$\frac{4 x^{7}}{({(5 y)}^{2} - 7 y^{2}) y}$

Step 2

Simplify the denominator.

Apply the product rule to $5 y$ .

$\frac{4 x^{7}}{(5^{2} y^{2} - 7 y^{2}) y}$

Raise $5$ to the power of $2$ .

$\frac{4 x^{7}}{(25 y^{2} - 7 y^{2}) y}$

Subtract $7 y^{2}$ from $25 y^{2}$ .

$\frac{4 x^{7}}{18 y^{2} y}$

Combine exponents.

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

$\frac{4 x^{7}}{18 (y^{1} y^{2})}$

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

$\frac{4 x^{7}}{18 y^{1 + 2}}$

Add $1$ and $2$ .

$\frac{4 x^{7}}{18 y^{3}}$

Step 3

Cancel the common factor of $4$ and $18$ .

Factor $2$ out of $4 x^{7}$ .

$\frac{2 (2 x^{7})}{18 y^{3}}$

Cancel the common factors.

Factor $2$ out of $18 y^{3}$ .

$\frac{2 (2 x^{7})}{2 (9 y^{3})}$

Cancel the common factor.

$\frac{2 (2 x^{7})}{2 (9 y^{3})}$

Rewrite the expression.

$\frac{2 x^{7}}{9 y^{3}}$