Algebra Examples

\frac{2^{- 4}}{4^{0}}

$\frac{2^{- 4}}{4^{0}}$

Step 1

Move

2^{- 4}

$2^{- 4}$ to the denominator using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

\frac{1}{4^{0} \cdot 2^{4}}

$\frac{1}{4^{0} \cdot 2^{4}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

\frac{1}{{(2^{2})}^{0} \cdot 2^{4}}

$\frac{1}{{(2^{2})}^{0} \cdot 2^{4}}$

Step 2.2

Multiply the exponents in

{(2^{2})}^{0}

${(2^{2})}^{0}$ .

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Step 2.2.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\frac{1}{2^{2 \cdot 0} \cdot 2^{4}}

$\frac{1}{2^{2 \cdot 0} \cdot 2^{4}}$

Step 2.2.2

Multiply

2

$2$ by

0

$0$ .

\frac{1}{2^{0} \cdot 2^{4}}

$\frac{1}{2^{0} \cdot 2^{4}}$

\frac{1}{2^{0} \cdot 2^{4}}

$\frac{1}{2^{0} \cdot 2^{4}}$

Step 2.3

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

\frac{1}{2^{0 + 4}}

$\frac{1}{2^{0 + 4}}$

Step 2.4

Add

0

$0$ and

4

$4$ .

\frac{1}{2^{4}}

$\frac{1}{2^{4}}$

\frac{1}{2^{4}}

$\frac{1}{2^{4}}$

Step 3

Raise

2

$2$ to the power of

4

$4$ .

\frac{1}{16}

$\frac{1}{16}$