Basic Math Examples

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

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

Step 1

Move

4^{- 4}

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

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

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

2 \cdot 4^{4}

$2 \cdot 4^{4}$

Step 2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

2 \cdot {(2^{2})}^{4}

$2 \cdot {(2^{2})}^{4}$

Step 3

Multiply the exponents in

{(2^{2})}^{4}

${(2^{2})}^{4}$ .

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Step 3.1

Apply the power rule and multiply exponents,

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

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

2 \cdot 2^{2 \cdot 4}

$2 \cdot 2^{2 \cdot 4}$

Step 3.2

Multiply

2

$2$ by

4

$4$ .

2 \cdot 2^{8}

$2 \cdot 2^{8}$

2 \cdot 2^{8}

$2 \cdot 2^{8}$

Step 4

Use the power rule

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

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

2^{1 + 8}

$2^{1 + 8}$

Step 5

Add

1

$1$ and

8

$8$ .

2^{9}

$2^{9}$

Step 6

Raise

2

$2$ to the power of

9

$9$ .

512

$512$