Simplify (6x^7y^5)/(3x^-1)

$\frac{6 x^{7} y^{5}}{3 x^{- 1}}$

Step 1

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

$\frac{6 x^{7} y^{5} x}{3}$

Step 2

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

Move $x$ .

$\frac{6 (x \cdot x^{7}) y^{5}}{3}$

Multiply $x$ by $x^{7}$ .

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

$\frac{6 (x^{1} x^{7}) y^{5}}{3}$

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

$\frac{6 x^{1 + 7} y^{5}}{3}$

Add $1$ and $7$ .

$\frac{6 x^{8} y^{5}}{3}$

Step 3

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 x^{8} y^{5}$ .

$\frac{3 (2 x^{8} y^{5})}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (2 x^{8} y^{5})}{3 (1)}$

Cancel the common factor.

$\frac{3 (2 x^{8} y^{5})}{3 \cdot 1}$

Rewrite the expression.

$\frac{2 x^{8} y^{5}}{1}$

Divide $2 x^{8} y^{5}$ by $1$ .

$2 x^{8} y^{5}$