Basic Math Examples

$\frac{1}{256} \div {(\frac{1}{4})}^{7}$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{1}{256}}{{(\frac{1}{4})}^{7}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{256} \cdot \frac{1}{{(\frac{1}{4})}^{7}}$

Step 3

Combine fractions.

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Step 3.1

Combine.

$\frac{1 \cdot 1}{256 {(\frac{1}{4})}^{7}}$

Step 3.2

Multiply

$1$ by

$1$ .

$\frac{1}{256 {(\frac{1}{4})}^{7}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite

$256$ as

$2^{8}$ .

$\frac{1}{2^{8} {(\frac{1}{4})}^{7}}$

Step 4.2

Rewrite

$\frac{1}{4}$ as

$4^{- 1}$ .

$\frac{1}{2^{8} {(4^{- 1})}^{7}}$

Step 4.3

Rewrite

$4$ as

$2^{2}$ .

$\frac{1}{2^{8} {({(2^{2})}^{- 1})}^{7}}$

Step 4.4

Apply the power rule and multiply exponents,

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

$\frac{1}{2^{8} {(2^{2 \cdot - 1})}^{7}}$

Step 4.5

Multiply

$2$ by

$- 1$ .

$\frac{1}{2^{8} {(2^{- 2})}^{7}}$

Step 4.6

Multiply the exponents in

${(2^{- 2})}^{7}$ .

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Step 4.6.1

Apply the power rule and multiply exponents,

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

$\frac{1}{2^{8} \cdot 2^{- 2 \cdot 7}}$

Step 4.6.2

Multiply

$- 2$ by

$7$ .

$\frac{1}{2^{8} \cdot 2^{- 14}}$

Step 4.7

Use the power rule

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

$\frac{1}{2^{8 - 14}}$

Step 4.8

Subtract

$14$ from

$8$ .

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

Step 5

Simplify the denominator.

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Step 5.1

Rewrite the expression using the negative exponent rule

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

$\frac{1}{\frac{1}{2^{6}}}$

Step 5.2

Raise

$2$ to the power of

$6$ .

$\frac{1}{\frac{1}{64}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$1 \cdot 64$

Step 7

Multiply

$64$ by

$1$ .

$64$