Simplify ((6x^3)^2)/((3x^2)^3)

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

Simplify the numerator.

Apply the product rule to $6 x^{3}$ .

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

Raise $6$ to the power of $2$ .

$\frac{36 {(x^{3})}^{2}}{{(3 x^{2})}^{3}}$

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

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

$\frac{36 x^{3 \cdot 2}}{{(3 x^{2})}^{3}}$

Multiply $3$ by $2$ .

$\frac{36 x^{6}}{{(3 x^{2})}^{3}}$

Simplify the denominator.

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

$\frac{36 x^{6}}{3^{3} {(x^{2})}^{3}}$

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

$\frac{36 x^{6}}{27 {(x^{2})}^{3}}$

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

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

$\frac{36 x^{6}}{27 x^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$\frac{36 x^{6}}{27 x^{6}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $36$ and $27$ .

Factor $9$ out of $36 x^{6}$ .

$\frac{9 (4 x^{6})}{27 x^{6}}$

Cancel the common factors.

Factor $9$ out of $27 x^{6}$ .

$\frac{9 (4 x^{6})}{9 (3 x^{6})}$

Cancel the common factor.

$\frac{9 (4 x^{6})}{9 (3 x^{6})}$

Rewrite the expression.

$\frac{4 x^{6}}{3 x^{6}}$

Cancel the common factor of $x^{6}$ .

Cancel the common factor.

$\frac{4 x^{6}}{3 x^{6}}$

Rewrite the expression.

$\frac{4}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$