Algebra Examples

${(\frac{192 x^{12}}{3 x^{3}})}^{\frac{1}{3}}$

Step 1

Cancel the common factor of $192$ and $3$ .

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Step 1.1

Factor $3$ out of $192 x^{12}$ .

${(\frac{3 (64 x^{12})}{3 x^{3}})}^{\frac{1}{3}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

${(\frac{3 (64 x^{12})}{3 (x^{3})})}^{\frac{1}{3}}$

Step 1.2.2

Cancel the common factor.

${(\frac{3 (64 x^{12})}{3 x^{3}})}^{\frac{1}{3}}$

Step 1.2.3

Rewrite the expression.

${(\frac{64 x^{12}}{x^{3}})}^{\frac{1}{3}}$

Step 2

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

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Step 2.1

Factor $x^{3}$ out of $64 x^{12}$ .

${(\frac{x^{3} (64 x^{9})}{x^{3}})}^{\frac{1}{3}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

${(\frac{x^{3} (64 x^{9})}{x^{3} \cdot 1})}^{\frac{1}{3}}$

Step 2.2.2

Cancel the common factor.

${(\frac{x^{3} (64 x^{9})}{x^{3} \cdot 1})}^{\frac{1}{3}}$

Step 2.2.3

Rewrite the expression.

${(\frac{64 x^{9}}{1})}^{\frac{1}{3}}$

Step 2.2.4

Divide $64 x^{9}$ by $1$ .

${(64 x^{9})}^{\frac{1}{3}}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $64 x^{9}$ .

$64^{\frac{1}{3}} {(x^{9})}^{\frac{1}{3}}$

Step 3.2

Rewrite $64$ as $4^{3}$ .

${(4^{3})}^{\frac{1}{3}} {(x^{9})}^{\frac{1}{3}}$

Step 3.3

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

$4^{3 (\frac{1}{3})} {(x^{9})}^{\frac{1}{3}}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

$4^{3 (\frac{1}{3})} {(x^{9})}^{\frac{1}{3}}$

Step 4.2

Rewrite the expression.

$4^{1} {(x^{9})}^{\frac{1}{3}}$

Step 5

Simplify the expression.

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Step 5.1

Evaluate the exponent.

$4 {(x^{9})}^{\frac{1}{3}}$

Step 5.2

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

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Step 5.2.1

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

$4 x^{9 (\frac{1}{3})}$

Step 5.2.2

Cancel the common factor of $3$ .

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Step 5.2.2.1

Factor $3$ out of $9$ .

$4 x^{3 (3) \frac{1}{3}}$

Step 5.2.2.2

Cancel the common factor.

$4 x^{3 \cdot 3 \frac{1}{3}}$

Step 5.2.2.3

Rewrite the expression.

$4 x^{3}$