Simplify ((3x^5yz^-1)/(15x^2y^6z^3))^-2

${(\frac{3 x^{5} y z^{- 1}}{15 x^{2} y^{6} z^{3}})}^{- 2}$

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

${(\frac{3 x^{5} y}{15 x^{2} y^{6} z^{3} z})}^{- 2}$

Multiply $z^{3}$ by $z$ by adding the exponents.

Move $z$ .

${(\frac{3 x^{5} y}{15 x^{2} y^{6} (z \cdot z^{3})})}^{- 2}$

Multiply $z$ by $z^{3}$ .

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

${(\frac{3 x^{5} y}{15 x^{2} y^{6} (z^{1} z^{3})})}^{- 2}$

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

${(\frac{3 x^{5} y}{15 x^{2} y^{6} z^{1 + 3}})}^{- 2}$

Add $1$ and $3$ .

${(\frac{3 x^{5} y}{15 x^{2} y^{6} z^{4}})}^{- 2}$

Cancel the common factor of $3$ and $15$ .

Factor $3$ out of $3 x^{5} y$ .

${(\frac{3 (x^{5} y)}{15 x^{2} y^{6} z^{4}})}^{- 2}$

Cancel the common factors.

Factor $3$ out of $15 x^{2} y^{6} z^{4}$ .

${(\frac{3 (x^{5} y)}{3 (5 x^{2} y^{6} z^{4})})}^{- 2}$

Cancel the common factor.

${(\frac{3 (x^{5} y)}{3 (5 x^{2} y^{6} z^{4})})}^{- 2}$

Rewrite the expression.

${(\frac{x^{5} y}{5 x^{2} y^{6} z^{4}})}^{- 2}$

Cancel the common factor of $x^{5}$ and $x^{2}$ .

Factor $x^{2}$ out of $x^{5} y$ .

${(\frac{x^{2} (x^{3} y)}{5 x^{2} y^{6} z^{4}})}^{- 2}$

Cancel the common factors.

Factor $x^{2}$ out of $5 x^{2} y^{6} z^{4}$ .

${(\frac{x^{2} (x^{3} y)}{x^{2} (5 y^{6} z^{4})})}^{- 2}$

Cancel the common factor.

${(\frac{x^{2} (x^{3} y)}{x^{2} (5 y^{6} z^{4})})}^{- 2}$

Rewrite the expression.

${(\frac{x^{3} y}{5 y^{6} z^{4}})}^{- 2}$

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

Factor $y$ out of $x^{3} y$ .

${(\frac{y x^{3}}{5 y^{6} z^{4}})}^{- 2}$

Cancel the common factors.

Factor $y$ out of $5 y^{6} z^{4}$ .

${(\frac{y x^{3}}{y (5 y^{5} z^{4})})}^{- 2}$

Cancel the common factor.

${(\frac{y x^{3}}{y (5 y^{5} z^{4})})}^{- 2}$

Rewrite the expression.

${(\frac{x^{3}}{5 y^{5} z^{4}})}^{- 2}$

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{5 y^{5} z^{4}}{x^{3}})}^{2}$

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

Apply the product rule to $\frac{5 y^{5} z^{4}}{x^{3}}$ .

$\frac{{(5 y^{5} z^{4})}^{2}}{{(x^{3})}^{2}}$

Apply the product rule to $5 y^{5} z^{4}$ .

$\frac{{(5 y^{5})}^{2} {(z^{4})}^{2}}{{(x^{3})}^{2}}$

Apply the product rule to $5 y^{5}$ .

$\frac{5^{2} {(y^{5})}^{2} {(z^{4})}^{2}}{{(x^{3})}^{2}}$

Simplify the numerator.

Raise $5$ to the power of $2$ .

$\frac{25 {(y^{5})}^{2} {(z^{4})}^{2}}{{(x^{3})}^{2}}$

Multiply the exponents in ${(y^{5})}^{2}$ .

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

$\frac{25 y^{5 \cdot 2} {(z^{4})}^{2}}{{(x^{3})}^{2}}$

Multiply $5$ by $2$ .

$\frac{25 y^{10} {(z^{4})}^{2}}{{(x^{3})}^{2}}$

Multiply the exponents in ${(z^{4})}^{2}$ .

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

$\frac{25 y^{10} z^{4 \cdot 2}}{{(x^{3})}^{2}}$

Multiply $4$ by $2$ .

$\frac{25 y^{10} z^{8}}{{(x^{3})}^{2}}$

Multiply the exponents in ${(x^{3})}^{2}$ .

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

$\frac{25 y^{10} z^{8}}{x^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{25 y^{10} z^{8}}{x^{6}}$

Simplify ((3x^5yz^-1)/(15x^2y^6z^3))^-2

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