Simplify ((6x^5z)^3)/(4x^4z^2)

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

Step 1

Simplify the numerator.

Apply the product rule to $6 x^{5} z$ .

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

Apply the product rule to $6 x^{5}$ .

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

Raise $6$ to the power of $3$ .

$\frac{216 {(x^{5})}^{3} z^{3}}{4 x^{4} z^{2}}$

Multiply the exponents in ${(x^{5})}^{3}$ .

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

$\frac{216 x^{5 \cdot 3} z^{3}}{4 x^{4} z^{2}}$

Multiply $5$ by $3$ .

$\frac{216 x^{15} z^{3}}{4 x^{4} z^{2}}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $216$ and $4$ .

Factor $4$ out of $216 x^{15} z^{3}$ .

$\frac{4 (54 x^{15} z^{3})}{4 x^{4} z^{2}}$

Cancel the common factors.

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

$\frac{4 (54 x^{15} z^{3})}{4 (x^{4} z^{2})}$

Cancel the common factor.

$\frac{4 (54 x^{15} z^{3})}{4 (x^{4} z^{2})}$

Rewrite the expression.

$\frac{54 x^{15} z^{3}}{x^{4} z^{2}}$

Cancel the common factor of $x^{15}$ and $x^{4}$ .

Factor $x^{4}$ out of $54 x^{15} z^{3}$ .

$\frac{x^{4} (54 x^{11} z^{3})}{x^{4} z^{2}}$

Cancel the common factors.

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

$\frac{x^{4} (54 x^{11} z^{3})}{x^{4} (z^{2})}$

Cancel the common factor.

$\frac{x^{4} (54 x^{11} z^{3})}{x^{4} z^{2}}$

Rewrite the expression.

$\frac{54 x^{11} z^{3}}{z^{2}}$

Cancel the common factor of $z^{3}$ and $z^{2}$ .

Factor $z^{2}$ out of $54 x^{11} z^{3}$ .

$\frac{z^{2} (54 x^{11} z)}{z^{2}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{z^{2} (54 x^{11} z)}{z^{2} \cdot 1}$

Cancel the common factor.

$\frac{z^{2} (54 x^{11} z)}{z^{2} \cdot 1}$

Rewrite the expression.

$\frac{54 x^{11} z}{1}$

Divide $54 x^{11} z$ by $1$ .

$54 x^{11} z$

Simplify ((6x^5z)^3)/(4x^4z^2)

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