Simplify (26x^-7y^5z^12)/(13x^4y^0z^8)

$\frac{26 x^{- 7} y^{5} z^{12}}{13 x^{4} y^{0} z^{8}}$

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

$\frac{26 y^{5} z^{12}}{13 x^{4} y^{0} z^{8} x^{7}}$

Simplify the denominator.

Multiply $x^{4}$ by $x^{7}$ by adding the exponents.

Move $x^{7}$ .

$\frac{26 y^{5} z^{12}}{13 (x^{7} x^{4}) y^{0} z^{8}}$

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

$\frac{26 y^{5} z^{12}}{13 x^{7 + 4} y^{0} z^{8}}$

Add $7$ and $4$ .

$\frac{26 y^{5} z^{12}}{13 x^{11} y^{0} z^{8}}$

Simplify $13 x^{11} y^{0} z^{8}$ .

$\frac{26 y^{5} z^{12}}{13 x^{11} z^{8}}$

Cancel the common factor of $26$ and $13$ .

Factor $13$ out of $26 y^{5} z^{12}$ .

$\frac{13 (2 y^{5} z^{12})}{13 x^{11} z^{8}}$

Cancel the common factors.

Factor $13$ out of $13 x^{11} z^{8}$ .

$\frac{13 (2 y^{5} z^{12})}{13 (x^{11} z^{8})}$

Cancel the common factor.

$\frac{13 (2 y^{5} z^{12})}{13 (x^{11} z^{8})}$

Rewrite the expression.

$\frac{2 y^{5} z^{12}}{x^{11} z^{8}}$

Cancel the common factor of $z^{12}$ and $z^{8}$ .

Factor $z^{8}$ out of $2 y^{5} z^{12}$ .

$\frac{z^{8} (2 y^{5} z^{4})}{x^{11} z^{8}}$

Cancel the common factors.

Factor $z^{8}$ out of $x^{11} z^{8}$ .

$\frac{z^{8} (2 y^{5} z^{4})}{z^{8} x^{11}}$

Cancel the common factor.

$\frac{z^{8} (2 y^{5} z^{4})}{z^{8} x^{11}}$

Rewrite the expression.

$\frac{2 y^{5} z^{4}}{x^{11}}$