Divide ((32x^3y)/(y^8))÷((y^7)/(8x^4))

$\frac{32 x^{3} y}{y^{8}} \div \frac{y^{7}}{8 x^{4}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{32 x^{3} y}{y^{8}} \cdot \frac{8 x^{4}}{y^{7}}$

Step 2

Combine.

$\frac{32 x^{3} y (8 x^{4})}{y^{8} y^{7}}$

Step 3

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

Move $x^{4}$ .

$\frac{32 (x^{4} x^{3}) y \cdot 8}{y^{8} y^{7}}$

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

$\frac{32 x^{4 + 3} y \cdot 8}{y^{8} y^{7}}$

Add $4$ and $3$ .

$\frac{32 x^{7} y \cdot 8}{y^{8} y^{7}}$

Step 4

Multiply $y^{8}$ by $y^{7}$ by adding the exponents.

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

$\frac{32 x^{7} y \cdot 8}{y^{8 + 7}}$

Add $8$ and $7$ .

$\frac{32 x^{7} y \cdot 8}{y^{15}}$

Step 5

Cancel the common factor of $y$ and $y^{15}$ .

Factor $y$ out of $32 x^{7} y \cdot 8$ .

$\frac{y (32 x^{7} \cdot 8)}{y^{15}}$

Cancel the common factors.

Factor $y$ out of $y^{15}$ .

$\frac{y (32 x^{7} \cdot 8)}{y \cdot y^{14}}$

Cancel the common factor.

$\frac{y (32 x^{7} \cdot 8)}{y \cdot y^{14}}$

Rewrite the expression.

$\frac{32 x^{7} \cdot 8}{y^{14}}$

Step 6

Multiply $8$ by $32$ .

$\frac{256 x^{7}}{y^{14}}$