Simplify (x^5y^4y^3z^4)/((x^2y^3)^2z^3)

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

Multiply $y^{4}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

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

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

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

Add $3$ and $4$ .

$\frac{x^{5} y^{7} z^{4}}{{(x^{2} y^{3})}^{2} z^{3}}$

Cancel the common factor of $z^{4}$ and $z^{3}$ .

Factor $z^{3}$ out of $x^{5} y^{7} z^{4}$ .

$\frac{z^{3} (x^{5} y^{7} z)}{{(x^{2} y^{3})}^{2} z^{3}}$

Cancel the common factors.

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

$\frac{z^{3} (x^{5} y^{7} z)}{z^{3} {(x^{2} y^{3})}^{2}}$

Cancel the common factor.

$\frac{z^{3} (x^{5} y^{7} z)}{z^{3} {(x^{2} y^{3})}^{2}}$

Rewrite the expression.

$\frac{x^{5} y^{7} z}{{(x^{2} y^{3})}^{2}}$

Simplify the denominator.

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

$\frac{x^{5} y^{7} z}{{(x^{2})}^{2} {(y^{3})}^{2}}$

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

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

$\frac{x^{5} y^{7} z}{x^{2 \cdot 2} {(y^{3})}^{2}}$

Multiply $2$ by $2$ .

$\frac{x^{5} y^{7} z}{x^{4} {(y^{3})}^{2}}$

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

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

$\frac{x^{5} y^{7} z}{x^{4} y^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{x^{5} y^{7} z}{x^{4} y^{6}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x^{5}$ and $x^{4}$ .

Factor $x^{4}$ out of $x^{5} y^{7} z$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x y^{7} z}{y^{6}}$

Cancel the common factor of $y^{7}$ and $y^{6}$ .

Factor $y^{6}$ out of $x y^{7} z$ .

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

Cancel the common factors.

Multiply by $1$ .

$\frac{y^{6} (x y z)}{y^{6} \cdot 1}$

Cancel the common factor.

$\frac{y^{6} (x y z)}{y^{6} \cdot 1}$

Rewrite the expression.

$\frac{x y z}{1}$

Divide $x y z$ by $1$ .

$x y z$

Simplify (x^5y^4y^3z^4)/((x^2y^3)^2z^3)

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