Algebra Examples

${(\frac{2 a^{4} b^{6} c^{2}}{6 a^{- 3} b^{4} c^{8}})}^{3}$

Step 1

Move $a^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{2 a^{4} b^{6} c^{2} a^{3}}{6 b^{4} c^{8}})}^{3}$

Step 2

Multiply $a^{4}$ by $a^{3}$ by adding the exponents.

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Step 2.1

Move $a^{3}$ .

${(\frac{2 (a^{3} a^{4}) b^{6} c^{2}}{6 b^{4} c^{8}})}^{3}$

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{2 a^{3 + 4} b^{6} c^{2}}{6 b^{4} c^{8}})}^{3}$

Step 2.3

Add $3$ and $4$ .

${(\frac{2 a^{7} b^{6} c^{2}}{6 b^{4} c^{8}})}^{3}$

Step 3

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

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Step 3.1

Factor $2$ out of $2 a^{7} b^{6} c^{2}$ .

${(\frac{2 (a^{7} b^{6} c^{2})}{6 b^{4} c^{8}})}^{3}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $6 b^{4} c^{8}$ .

${(\frac{2 (a^{7} b^{6} c^{2})}{2 (3 b^{4} c^{8})})}^{3}$

Step 3.2.2

Cancel the common factor.

${(\frac{2 (a^{7} b^{6} c^{2})}{2 (3 b^{4} c^{8})})}^{3}$

Step 3.2.3

Rewrite the expression.

${(\frac{a^{7} b^{6} c^{2}}{3 b^{4} c^{8}})}^{3}$

Step 4

Cancel the common factor of $b^{6}$ and $b^{4}$ .

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Step 4.1

Factor $b^{4}$ out of $a^{7} b^{6} c^{2}$ .

${(\frac{b^{4} (a^{7} b^{2} c^{2})}{3 b^{4} c^{8}})}^{3}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $b^{4}$ out of $3 b^{4} c^{8}$ .

${(\frac{b^{4} (a^{7} b^{2} c^{2})}{b^{4} (3 c^{8})})}^{3}$

Step 4.2.2

Cancel the common factor.

${(\frac{b^{4} (a^{7} b^{2} c^{2})}{b^{4} (3 c^{8})})}^{3}$

Step 4.2.3

Rewrite the expression.

${(\frac{a^{7} b^{2} c^{2}}{3 c^{8}})}^{3}$

Step 5

Cancel the common factor of $c^{2}$ and $c^{8}$ .

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Step 5.1

Factor $c^{2}$ out of $a^{7} b^{2} c^{2}$ .

${(\frac{c^{2} (a^{7} b^{2})}{3 c^{8}})}^{3}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $c^{2}$ out of $3 c^{8}$ .

${(\frac{c^{2} (a^{7} b^{2})}{c^{2} (3 c^{6})})}^{3}$

Step 5.2.2

Cancel the common factor.

${(\frac{c^{2} (a^{7} b^{2})}{c^{2} (3 c^{6})})}^{3}$

Step 5.2.3

Rewrite the expression.

${(\frac{a^{7} b^{2}}{3 c^{6}})}^{3}$

Step 6

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

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Step 6.1

Apply the product rule to $\frac{a^{7} b^{2}}{3 c^{6}}$ .

$\frac{{(a^{7} b^{2})}^{3}}{{(3 c^{6})}^{3}}$

Step 6.2

Apply the product rule to $a^{7} b^{2}$ .

$\frac{{(a^{7})}^{3} {(b^{2})}^{3}}{{(3 c^{6})}^{3}}$

Step 6.3

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

$\frac{{(a^{7})}^{3} {(b^{2})}^{3}}{3^{3} {(c^{6})}^{3}}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply the exponents in ${(a^{7})}^{3}$ .

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Step 7.1.1

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

$\frac{a^{7 \cdot 3} {(b^{2})}^{3}}{3^{3} {(c^{6})}^{3}}$

Step 7.1.2

Multiply $7$ by $3$ .

$\frac{a^{21} {(b^{2})}^{3}}{3^{3} {(c^{6})}^{3}}$

Step 7.2

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

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Step 7.2.1

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

$\frac{a^{21} b^{2 \cdot 3}}{3^{3} {(c^{6})}^{3}}$

Step 7.2.2

Multiply $2$ by $3$ .

$\frac{a^{21} b^{6}}{3^{3} {(c^{6})}^{3}}$

Step 8

Simplify the denominator.

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Step 8.1

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

$\frac{a^{21} b^{6}}{27 {(c^{6})}^{3}}$

Step 8.2

Multiply the exponents in ${(c^{6})}^{3}$ .

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Step 8.2.1

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

$\frac{a^{21} b^{6}}{27 c^{6 \cdot 3}}$

Step 8.2.2

Multiply $6$ by $3$ .

$\frac{a^{21} b^{6}}{27 c^{18}}$