Basic Math Examples

${(8 a^{- 3})}^{4} {(a^{5})}^{- 3}$

Step 1

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

${(8 \frac{1}{a^{3}})}^{4} {(a^{5})}^{- 3}$

Step 2

Combine $8$ and $\frac{1}{a^{3}}$ .

${(\frac{8}{a^{3}})}^{4} {(a^{5})}^{- 3}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{8}{a^{3}}$ .

$\frac{8^{4}}{{(a^{3})}^{4}} {(a^{5})}^{- 3}$

Step 3.2

Raise $8$ to the power of $4$ .

$\frac{4096}{{(a^{3})}^{4}} {(a^{5})}^{- 3}$

Step 3.3

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

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Step 3.3.1

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

$\frac{4096}{a^{3 \cdot 4}} {(a^{5})}^{- 3}$

Step 3.3.2

Multiply $3$ by $4$ .

$\frac{4096}{a^{12}} {(a^{5})}^{- 3}$

Step 3.4

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

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Step 3.4.1

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

$\frac{4096}{a^{12}} a^{5 \cdot - 3}$

Step 3.4.2

Multiply $5$ by $- 3$ .

$\frac{4096}{a^{12}} a^{- 15}$

Step 4

Cancel the common factor of $a^{- 15}$ .

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Step 4.1

Factor $a^{- 15}$ out of $a^{12}$ .

$\frac{4096}{a^{- 15} a^{27}} a^{- 15}$

Step 4.2

Cancel the common factor.

$\frac{4096}{a^{- 15} a^{27}} a^{- 15}$

Step 4.3

Rewrite the expression.

$\frac{4096}{a^{27}}$