Pre-Algebra Examples

${(\frac{6 x^{3}}{- 2 x^{8}})}^{3}$

Step 1

Cancel the common factor of $6$ and $- 2$ .

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Step 1.1

Factor $2$ out of $6 x^{3}$ .

${(\frac{2 (3 x^{3})}{- 2 x^{8}})}^{3}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $- 2 x^{8}$ .

${(\frac{2 (3 x^{3})}{2 (- x^{8})})}^{3}$

Step 1.2.2

Cancel the common factor.

${(\frac{2 (3 x^{3})}{2 (- x^{8})})}^{3}$

Step 1.2.3

Rewrite the expression.

${(\frac{3 x^{3}}{- x^{8}})}^{3}$

Step 2

Cancel the common factor of $x^{3}$ and $x^{8}$ .

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Step 2.1

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

${(\frac{x^{3} \cdot 3}{- x^{8}})}^{3}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x^{3}$ out of $- x^{8}$ .

${(\frac{x^{3} \cdot 3}{x^{3} (- x^{5})})}^{3}$

Step 2.2.2

Cancel the common factor.

${(\frac{x^{3} \cdot 3}{x^{3} (- x^{5})})}^{3}$

Step 2.2.3

Rewrite the expression.

${(\frac{3}{- x^{5}})}^{3}$

Step 3

Move the negative in front of the fraction.

${(- \frac{3}{x^{5}})}^{3}$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 4.1

Apply the product rule to $- \frac{3}{x^{5}}$ .

${(- 1)}^{3} {(\frac{3}{x^{5}})}^{3}$

Step 4.2

Apply the product rule to $\frac{3}{x^{5}}$ .

${(- 1)}^{3} \frac{3^{3}}{{(x^{5})}^{3}}$

Step 5

Raise $- 1$ to the power of $3$ .

$- \frac{3^{3}}{{(x^{5})}^{3}}$

Step 6

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

$- \frac{27}{{(x^{5})}^{3}}$

Step 7

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

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Step 7.1

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

$- \frac{27}{x^{5 \cdot 3}}$

Step 7.2

Multiply $5$ by $3$ .

$- \frac{27}{x^{15}}$