Simplify (24x^-1)/(8x^-5y^7)

$\frac{24 x^{- 1}}{8 x^{- 5} y^{7}}$

Step 1

Move $x^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{24 x^{- 1} x^{5}}{8 y^{7}}$

Step 2

Multiply $x^{- 1}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$\frac{24 (x^{5} x^{- 1})}{8 y^{7}}$

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

$\frac{24 x^{5 - 1}}{8 y^{7}}$

Subtract $1$ from $5$ .

$\frac{24 x^{4}}{8 y^{7}}$

Step 3

Cancel the common factor of $24$ and $8$ .

Factor $8$ out of $24 x^{4}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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