Algebra Examples

${(4 a^{2} b^{0} c^{- 5})}^{3}$

Step 1

Anything raised to $0$ is $1$ .

${(4 a^{2} \cdot 1 c^{- 5})}^{3}$

Step 2

Multiply $4$ by $1$ .

${(4 a^{2} c^{- 5})}^{3}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(4 a^{2} \frac{1}{c^{5}})}^{3}$

Step 4

Multiply $4 a^{2} \frac{1}{c^{5}}$ .

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Step 4.1

Combine $4$ and $\frac{1}{c^{5}}$ .

${(a^{2} \frac{4}{c^{5}})}^{3}$

Step 4.2

Combine $a^{2}$ and $\frac{4}{c^{5}}$ .

${(\frac{a^{2} \cdot 4}{c^{5}})}^{3}$

Step 5

Move $4$ to the left of $a^{2}$ .

${(\frac{4 \cdot a^{2}}{c^{5}})}^{3}$

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 $\frac{4 a^{2}}{c^{5}}$ .

$\frac{{(4 a^{2})}^{3}}{{(c^{5})}^{3}}$

Step 6.2

Apply the product rule to $4 a^{2}$ .

$\frac{4^{3} {(a^{2})}^{3}}{{(c^{5})}^{3}}$

Step 7

Simplify the numerator.

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Step 7.1

Raise $4$ to the power of $3$ .

$\frac{64 {(a^{2})}^{3}}{{(c^{5})}^{3}}$

Step 7.2

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

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Step 7.2.1

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

$\frac{64 a^{2 \cdot 3}}{{(c^{5})}^{3}}$

Step 7.2.2

Multiply $2$ by $3$ .

$\frac{64 a^{6}}{{(c^{5})}^{3}}$

Step 8

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

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Step 8.1

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

$\frac{64 a^{6}}{c^{5 \cdot 3}}$

Step 8.2

Multiply $5$ by $3$ .

$\frac{64 a^{6}}{c^{15}}$