Basic Math Examples

$(2^{3} - 2^{- 4}) \div 2^{- 5}$

Step 1

Rewrite the division as a fraction.

$\frac{2^{3} - 2^{- 4}}{2^{- 5}}$

Step 2

Move $2^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$(2^{3} - 2^{- 4}) \cdot 2^{5}$

Step 3

Simplify each term.

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Step 3.1

Raise $2$ to the power of $3$ .

$(8 - 2^{- 4}) \cdot 2^{5}$

Step 3.2

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

$(8 - \frac{1}{2^{4}}) \cdot 2^{5}$

Step 3.3

Raise $2$ to the power of $4$ .

$(8 - \frac{1}{16}) \cdot 2^{5}$

Step 4

To write $8$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$(8 \cdot \frac{16}{16} - \frac{1}{16}) \cdot 2^{5}$

Step 5

Combine $8$ and $\frac{16}{16}$ .

$(\frac{8 \cdot 16}{16} - \frac{1}{16}) \cdot 2^{5}$

Step 6

Combine the numerators over the common denominator.

$\frac{8 \cdot 16 - 1}{16} \cdot 2^{5}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $8$ by $16$ .

$\frac{128 - 1}{16} \cdot 2^{5}$

Step 7.2

Subtract $1$ from $128$ .

$\frac{127}{16} \cdot 2^{5}$

Step 8

Raise $2$ to the power of $5$ .

$\frac{127}{16} \cdot 32$

Step 9

Cancel the common factor of $16$ .

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Step 9.1

Factor $16$ out of $32$ .

$\frac{127}{16} \cdot (16 (2))$

Step 9.2

Cancel the common factor.

$\frac{127}{16} \cdot (16 \cdot 2)$

Step 9.3

Rewrite the expression.

$127 \cdot 2$

Step 10

Multiply $127$ by $2$ .

$254$