Calculus Examples

$\frac{4^{- 3}}{2^{- 8}}$

Step 1

Move $4^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{2^{- 8} \cdot 4^{3}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $4$ as $2^{2}$ .

$\frac{1}{2^{- 8} \cdot {(2^{2})}^{3}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{1}{2^{- 8} \cdot 2^{2 \cdot 3}}$

Step 2.2.2

Multiply $2$ by $3$ .

$\frac{1}{2^{- 8} \cdot 2^{6}}$

Step 2.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{2^{- 8 + 6}}$

Step 2.4

Add $- 8$ and $6$ .

$\frac{1}{2^{- 2}}$

Step 3

Move $2^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$2^{2}$

Step 4

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

$4$