Pre-Algebra Examples

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

Step 1

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

${(4 \frac{1}{a^{3}})}^{0} {(- 5 a^{- 4})}^{3}$

Step 2

Combine fractions.

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Step 2.1

Combine $4$ and $\frac{1}{a^{3}}$ .

${(\frac{4}{a^{3}})}^{0} {(- 5 a^{- 4})}^{3}$

Step 2.2

Simplify the expression.

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Step 2.2.1

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

$\frac{4^{0}}{{(a^{3})}^{0}} {(- 5 a^{- 4})}^{3}$

Step 2.2.2

Anything raised to $0$ is $1$ .

$\frac{1}{{(a^{3})}^{0}} {(- 5 a^{- 4})}^{3}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply the exponents in ${(a^{3})}^{0}$ .

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Step 3.1.1

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

$\frac{1}{a^{3 \cdot 0}} {(- 5 a^{- 4})}^{3}$

Step 3.1.2

Multiply $3$ by $0$ .

$\frac{1}{a^{0}} {(- 5 a^{- 4})}^{3}$

Step 3.2

Anything raised to $0$ is $1$ .

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

Step 4

Simplify the expression.

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Step 4.1

Divide $1$ by $1$ .

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

Step 4.2

Multiply ${(- 5 a^{- 4})}^{3}$ by $1$ .

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

Step 5

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

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

Step 6

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

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

Step 7

Move the negative in front of the fraction.

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

Step 8

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

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Step 8.1

Apply the product rule to $- \frac{5}{a^{4}}$ .

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

Step 8.2

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

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

Step 9

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

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

Step 10

Raise $5$ to the power of $3$ .

$- \frac{125}{{(a^{4})}^{3}}$

Step 11

Multiply the exponents in ${(a^{4})}^{3}$ .

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Step 11.1

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

$- \frac{125}{a^{4 \cdot 3}}$

Step 11.2

Multiply $4$ by $3$ .

$- \frac{125}{a^{12}}$