Simplify ((2x^3z^2)^3)/(x^3y^4z^2*x^-4z^3)

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

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

Move $x^{- 4}$ .

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

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

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

Add $- 4$ and $3$ .

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

Multiply $z^{2}$ by $z^{3}$ by adding the exponents.

Move $z^{3}$ .

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

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

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

Add $3$ and $2$ .

$\frac{{(2 x^{3} z^{2})}^{3}}{x^{- 1} y^{4} z^{5}}$

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

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

Simplify the numerator.

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

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

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

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

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

$\frac{8 {(x^{3})}^{3} {(z^{2})}^{3} x}{y^{4} z^{5}}$

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

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

$\frac{8 x^{3 \cdot 3} {(z^{2})}^{3} x}{y^{4} z^{5}}$

Multiply $3$ by $3$ .

$\frac{8 x^{9} {(z^{2})}^{3} x}{y^{4} z^{5}}$

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

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

$\frac{8 x^{9} z^{2 \cdot 3} x}{y^{4} z^{5}}$

Multiply $2$ by $3$ .

$\frac{8 x^{9} z^{6} x}{y^{4} z^{5}}$

Combine exponents.

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

$\frac{8 (x^{1} x^{9}) z^{6}}{y^{4} z^{5}}$

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

$\frac{8 x^{1 + 9} z^{6}}{y^{4} z^{5}}$

Add $1$ and $9$ .

$\frac{8 x^{10} z^{6}}{y^{4} z^{5}}$

Cancel the common factor of $z^{6}$ and $z^{5}$ .

Factor $z^{5}$ out of $8 x^{10} z^{6}$ .

$\frac{z^{5} (8 x^{10} z)}{y^{4} z^{5}}$

Cancel the common factors.

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

$\frac{z^{5} (8 x^{10} z)}{z^{5} y^{4}}$

Cancel the common factor.

$\frac{z^{5} (8 x^{10} z)}{z^{5} y^{4}}$

Rewrite the expression.

$\frac{8 x^{10} z}{y^{4}}$

Simplify ((2x^3z^2)^3)/(x^3y^4z^2*x^-4z^3)

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