Basic Math Examples

${(4 a^{- 1} b^{5} c^{- 3})}^{3}$

Step 1

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

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

Step 2

Combine $4$ and $\frac{1}{a}$ .

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

Step 3

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

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

Step 4

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

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

Step 5

Combine.

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

Step 6

Multiply $4$ by $1$ .

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

Step 7

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

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Step 7.1

Apply the product rule to $\frac{4 b^{5}}{a c^{3}}$ .

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

Step 7.2

Apply the product rule to $4 b^{5}$ .

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

Step 7.3

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

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

Step 8

Simplify the numerator.

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Step 8.1

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

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

Step 8.2

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

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Step 8.2.1

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

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

Step 8.2.2

Multiply $5$ by $3$ .

$\frac{64 b^{15}}{a^{3} {(c^{3})}^{3}}$

Step 9

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

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Step 9.1

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

$\frac{64 b^{15}}{a^{3} c^{3 \cdot 3}}$

Step 9.2

Multiply $3$ by $3$ .

$\frac{64 b^{15}}{a^{3} c^{9}}$