Algebra Examples

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

Step 1

Multiply $- \frac{2}{3} (a^{2} b^{3} c^{2})$ .

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Step 1.1

Combine $a^{2}$ and $\frac{2}{3}$ .

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

Step 1.2

Combine $b^{3}$ and $\frac{a^{2} \cdot 2}{3}$ .

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

Step 1.3

Combine $c^{2}$ and $\frac{b^{3} (a^{2} \cdot 2)}{3}$ .

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

Step 2

Move $2$ to the left of $c^{2} b^{3} a^{2}$ .

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

Step 3

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

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Step 3.1

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

${(- 1)}^{3} {(\frac{2 c^{2} b^{3} a^{2}}{3})}^{3}$

Step 3.2

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

${(- 1)}^{3} \frac{{(2 c^{2} b^{3} a^{2})}^{3}}{3^{3}}$

Step 3.3

Apply the product rule to $2 c^{2} b^{3} a^{2}$ .

${(- 1)}^{3} \frac{{(2 c^{2} b^{3})}^{3} {(a^{2})}^{3}}{3^{3}}$

Step 3.4

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

${(- 1)}^{3} \frac{{(2 c^{2})}^{3} {(b^{3})}^{3} {(a^{2})}^{3}}{3^{3}}$

Step 3.5

Apply the product rule to $2 c^{2}$ .

${(- 1)}^{3} \frac{2^{3} {(c^{2})}^{3} {(b^{3})}^{3} {(a^{2})}^{3}}{3^{3}}$

Step 4

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

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

Step 5

Simplify the numerator.

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Step 5.1

Raise $2$ to the power of $3$ .

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

Step 5.2

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

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Step 5.2.1

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

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

Step 5.2.2

Multiply $2$ by $3$ .

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

Step 5.3

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

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Step 5.3.1

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

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

Step 5.3.2

Multiply $3$ by $3$ .

$- \frac{8 c^{6} b^{9} {(a^{2})}^{3}}{3^{3}}$

Step 5.4

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

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Step 5.4.1

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

$- \frac{8 c^{6} b^{9} a^{2 \cdot 3}}{3^{3}}$

Step 5.4.2

Multiply $2$ by $3$ .

$- \frac{8 c^{6} b^{9} a^{6}}{3^{3}}$

Step 6

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

$- \frac{8 c^{6} b^{9} a^{6}}{27}$