Simplify ((3x^3y^2z^6)/(xy^-2z^3))^2

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

Move $y^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

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

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

${(\frac{3 x^{3} y^{2 + 2} z^{6}}{x z^{3}})}^{2}$

Add $2$ and $2$ .

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $z^{6}$ and $z^{3}$ .

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

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $3 x^{2} y^{4} z^{3}$ by $1$ .

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

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

Apply the product rule to $3 x^{2} y^{4} z^{3}$ .

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

Apply the product rule to $3 x^{2} y^{4}$ .

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

Apply the product rule to $3 x^{2}$ .

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

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

$9 {(x^{2})}^{2} {(y^{4})}^{2} {(z^{3})}^{2}$

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

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

$9 x^{2 \cdot 2} {(y^{4})}^{2} {(z^{3})}^{2}$

Multiply $2$ by $2$ .

$9 x^{4} {(y^{4})}^{2} {(z^{3})}^{2}$

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

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

$9 x^{4} y^{4 \cdot 2} {(z^{3})}^{2}$

Multiply $4$ by $2$ .

$9 x^{4} y^{8} {(z^{3})}^{2}$

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

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

$9 x^{4} y^{8} z^{3 \cdot 2}$

Multiply $3$ by $2$ .

$9 x^{4} y^{8} z^{6}$

Simplify ((3x^3y^2z^6)/(xy^-2z^3))^2

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