Simplify (22y^6z^8)/(2yz^-7)

$\frac{22 y^{6} z^{8}}{2 y z^{- 7}}$

Move $z^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{22 y^{6} z^{8} z^{7}}{2 y}$

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

Move $z^{7}$ .

$\frac{22 y^{6} (z^{7} z^{8})}{2 y}$

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

$\frac{22 y^{6} z^{7 + 8}}{2 y}$

Add $7$ and $8$ .

$\frac{22 y^{6} z^{15}}{2 y}$

Cancel the common factor of $22$ and $2$ .

Factor $2$ out of $22 y^{6} z^{15}$ .

$\frac{2 (11 y^{6} z^{15})}{2 y}$

Cancel the common factors.

Factor $2$ out of $2 y$ .

$\frac{2 (11 y^{6} z^{15})}{2 (y)}$

Cancel the common factor.

$\frac{2 (11 y^{6} z^{15})}{2 y}$

Rewrite the expression.

$\frac{11 y^{6} z^{15}}{y}$

Cancel the common factor of $y^{6}$ and $y$ .

Factor $y$ out of $11 y^{6} z^{15}$ .

$\frac{y (11 y^{5} z^{15})}{y}$

Cancel the common factors.

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

$\frac{y (11 y^{5} z^{15})}{y^{1}}$

Factor $y$ out of $y^{1}$ .

$\frac{y (11 y^{5} z^{15})}{y \cdot 1}$

Cancel the common factor.

$\frac{y (11 y^{5} z^{15})}{y \cdot 1}$

Rewrite the expression.

$\frac{11 y^{5} z^{15}}{1}$

Divide $11 y^{5} z^{15}$ by $1$ .

$11 y^{5} z^{15}$