Simplify ((81x^12)/(3x^3))^(1/3)

${(\frac{81 x^{12}}{3 x^{3}})}^{\frac{1}{3}}$

Step 1

Cancel the common factor of $81$ and $3$ .

Factor $3$ out of $81 x^{12}$ .

${(\frac{3 (27 x^{12})}{3 x^{3}})}^{\frac{1}{3}}$

Cancel the common factors.

Factor $3$ out of $3 x^{3}$ .

${(\frac{3 (27 x^{12})}{3 (x^{3})})}^{\frac{1}{3}}$

Cancel the common factor.

${(\frac{3 (27 x^{12})}{3 x^{3}})}^{\frac{1}{3}}$

Rewrite the expression.

${(\frac{27 x^{12}}{x^{3}})}^{\frac{1}{3}}$

Step 2

Cancel the common factor of $x^{12}$ and $x^{3}$ .

Factor $x^{3}$ out of $27 x^{12}$ .

${(\frac{x^{3} (27 x^{9})}{x^{3}})}^{\frac{1}{3}}$

Cancel the common factors.

Multiply by $1$ .

${(\frac{x^{3} (27 x^{9})}{x^{3} \cdot 1})}^{\frac{1}{3}}$

Cancel the common factor.

${(\frac{x^{3} (27 x^{9})}{x^{3} \cdot 1})}^{\frac{1}{3}}$

Rewrite the expression.

${(\frac{27 x^{9}}{1})}^{\frac{1}{3}}$

Divide $27 x^{9}$ by $1$ .

${(27 x^{9})}^{\frac{1}{3}}$

Step 3

Simplify the expression.

Apply the product rule to $27 x^{9}$ .

$27^{\frac{1}{3}} {(x^{9})}^{\frac{1}{3}}$

Rewrite $27$ as $3^{3}$ .

${(3^{3})}^{\frac{1}{3}} {(x^{9})}^{\frac{1}{3}}$

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

$3^{3 (\frac{1}{3})} {(x^{9})}^{\frac{1}{3}}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$3^{3 (\frac{1}{3})} {(x^{9})}^{\frac{1}{3}}$

Rewrite the expression.

$3^{1} {(x^{9})}^{\frac{1}{3}}$

Step 5

Evaluate the exponent.

$3 {(x^{9})}^{\frac{1}{3}}$

Step 6

Multiply the exponents in ${(x^{9})}^{\frac{1}{3}}$ .

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

$3 x^{9 (\frac{1}{3})}$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$3 x^{3 (3) \frac{1}{3}}$

Cancel the common factor.

$3 x^{3 \cdot 3 \frac{1}{3}}$

Rewrite the expression.

$3 x^{3}$

Simplify ((81x^12)/(3x^3))^(1/3)

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