Simplify ((x^2yz)^2(xy^2z^2))/((xyz)^2)

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

Simplify the numerator.

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

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

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

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Move $z^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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

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

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

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

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

Multiply $2$ by $2$ .

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

Simplify the denominator.

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Apply the product rule to $x y z$ .

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

Apply the product rule to $x y$ .

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

Simplify the numerator.

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

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Move $x$ .

$\frac{x \cdot x^{4} y^{2} z^{4} y^{2}}{x^{2} y^{2} z^{2}}$

Multiply $x$ by $x^{4}$ .

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

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

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

$\frac{x^{1 + 4} y^{2} z^{4} y^{2}}{x^{2} y^{2} z^{2}}$

Add $1$ and $4$ .

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

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

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Move $y^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Reduce the expression by cancelling the common factors.

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $y^{4}$ and $y^{2}$ .

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

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

Cancel the common factors.

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Factor $y^{2}$ out of $y^{2} z^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $z^{4}$ and $z^{2}$ .

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

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

Cancel the common factors.

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Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

$x^{3} y^{2} z^{2}$

Simplify ((x^2yz)^2(xy^2z^2))/((xyz)^2)

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