Simplify ((2x^-1yz^4)^3)/(6x^7yz^-10)

$\frac{{(2 x^{- 1} y z^{4})}^{3}}{6 x^{7} y z^{- 10}}$

Move $z^{- 10}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(2 x^{- 1} y z^{4})}^{3} z^{10}}{6 x^{7} y}$

Simplify the numerator.

Apply the product rule to $2 x^{- 1} y z^{4}$ .

$\frac{{(2 x^{- 1} y)}^{3} {(z^{4})}^{3} z^{10}}{6 x^{7} y}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{{(2 \frac{1}{x} y)}^{3} {(z^{4})}^{3} z^{10}}{6 x^{7} y}$

Combine $2$ and $\frac{1}{x}$ .

$\frac{{(\frac{2}{x} y)}^{3} {(z^{4})}^{3} z^{10}}{6 x^{7} y}$

Combine $\frac{2}{x}$ and $y$ .

$\frac{{(\frac{2 y}{x})}^{3} {(z^{4})}^{3} z^{10}}{6 x^{7} y}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{2 y}{x}$ .

$\frac{\frac{{(2 y)}^{3}}{x^{3}} {(z^{4})}^{3} z^{10}}{6 x^{7} y}$

Apply the product rule to $2 y$ .

$\frac{\frac{2^{3} y^{3}}{x^{3}} {(z^{4})}^{3} z^{10}}{6 x^{7} y}$

Raise $2$ to the power of $3$ .

$\frac{\frac{8 y^{3}}{x^{3}} {(z^{4})}^{3} z^{10}}{6 x^{7} y}$

Multiply the exponents in ${(z^{4})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\frac{8 y^{3}}{x^{3}} z^{4 \cdot 3} z^{10}}{6 x^{7} y}$

Multiply $4$ by $3$ .

$\frac{\frac{8 y^{3}}{x^{3}} z^{12} z^{10}}{6 x^{7} y}$

Combine exponents.

Combine $\frac{8 y^{3}}{x^{3}}$ and $z^{12}$ .

$\frac{\frac{8 y^{3} z^{12}}{x^{3}} z^{10}}{6 x^{7} y}$

Combine $\frac{8 y^{3} z^{12}}{x^{3}}$ and $z^{10}$ .

$\frac{\frac{8 y^{3} z^{12} z^{10}}{x^{3}}}{6 x^{7} y}$

Multiply $z^{12}$ by $z^{10}$ by adding the exponents.

Move $z^{10}$ .

$\frac{\frac{8 y^{3} (z^{10} z^{12})}{x^{3}}}{6 x^{7} y}$

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

$\frac{\frac{8 y^{3} z^{10 + 12}}{x^{3}}}{6 x^{7} y}$

Add $10$ and $12$ .

$\frac{\frac{8 y^{3} z^{22}}{x^{3}}}{6 x^{7} y}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{8 y^{3} z^{22}}{x^{3}} \cdot \frac{1}{6 x^{7} y}$

Combine.

$\frac{8 y^{3} z^{22} \cdot 1}{x^{3} (6 x^{7} y)}$

Multiply $x^{3}$ by $x^{7}$ by adding the exponents.

Move $x^{7}$ .

$\frac{8 y^{3} z^{22} \cdot 1}{x^{7} x^{3} (6 y)}$

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

$\frac{8 y^{3} z^{22} \cdot 1}{x^{7 + 3} (6 y)}$

Add $7$ and $3$ .

$\frac{8 y^{3} z^{22} \cdot 1}{x^{10} (6 y)}$

Multiply $8 y^{3} z^{22}$ by $1$ .

$\frac{8 y^{3} z^{22}}{x^{10} (6 y)}$

Cancel the common factor of $8$ and $6$ .

Factor $2$ out of $8 y^{3} z^{22}$ .

$\frac{2 (4 y^{3} z^{22})}{x^{10} (6 y)}$

Cancel the common factors.

Factor $2$ out of $x^{10} (6 y)$ .

$\frac{2 (4 y^{3} z^{22})}{2 (x^{10} (3 y))}$

Cancel the common factor.

$\frac{2 (4 y^{3} z^{22})}{2 (x^{10} (3 y))}$

Rewrite the expression.

$\frac{4 y^{3} z^{22}}{x^{10} (3 y)}$

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

Factor $y$ out of $4 y^{3} z^{22}$ .

$\frac{y (4 y^{2} z^{22})}{x^{10} (3 y)}$

Cancel the common factors.

Factor $y$ out of $x^{10} (3 y)$ .

$\frac{y (4 y^{2} z^{22})}{y (x^{10} \cdot (3))}$

Cancel the common factor.

$\frac{y (4 y^{2} z^{22})}{y (x^{10} \cdot (3))}$

Rewrite the expression.

$\frac{4 y^{2} z^{22}}{x^{10} \cdot (3)}$

Move $3$ to the left of $x^{10}$ .

$\frac{4 y^{2} z^{22}}{3 x^{10}}$

Simplify ((2x^-1yz^4)^3)/(6x^7yz^-10)

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