Simplify (y^11)/(4z^3)*(8z^7)/(y^7)

$\frac{y^{11}}{4 z^{3}} \cdot \frac{8 z^{7}}{y^{7}}$

Step 1

Combine.

$\frac{y^{11} (8 z^{7})}{4 z^{3} y^{7}}$

Step 2

Cancel the common factor of $y^{11}$ and $y^{7}$ .

Factor $y^{7}$ out of $y^{11} (8 z^{7})$ .

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

Cancel the common factors.

Factor $y^{7}$ out of $4 z^{3} y^{7}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $8$ and $4$ .

Factor $4$ out of $y^{4} (8 z^{7})$ .

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

Cancel the common factors.

Factor $4$ out of $4 z^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Cancel the common factor of $z^{7}$ and $z^{3}$ .

Factor $z^{3}$ out of $y^{4} (2 z^{7})$ .

$\frac{z^{3} (y^{4} (2 z^{4}))}{z^{3}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{z^{3} (y^{4} (2 z^{4}))}{z^{3} \cdot 1}$

Cancel the common factor.

$\frac{z^{3} (y^{4} (2 z^{4}))}{z^{3} \cdot 1}$

Rewrite the expression.

$\frac{y^{4} (2 z^{4})}{1}$

Divide $y^{4} (2 z^{4})$ by $1$ .

$y^{4} (2 z^{4})$

Step 5

Rewrite using the commutative property of multiplication.

$2 y^{4} z^{4}$