Basic Math Examples

\frac{2^{- 20} - 2^{- 22}}{2^{- 21}}

$\frac{2^{- 20} - 2^{- 22}}{2^{- 21}}$

Step 1

Move

$2^{- 21}$ to the numerator using the negative exponent rule

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

$(2^{- 20} - 2^{- 22}) \cdot 2^{21}$

Step 2

Simplify each term.

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Step 2.1

Rewrite the expression using the negative exponent rule

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

$(\frac{1}{2^{20}} - 2^{- 22}) \cdot 2^{21}$

Step 2.2

Raise

$2$ to the power of

$20$ .

$(\frac{1}{1048576} - 2^{- 22}) \cdot 2^{21}$

Step 2.3

Rewrite the expression using the negative exponent rule

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

$(\frac{1}{1048576} - \frac{1}{2^{22}}) \cdot 2^{21}$

Step 2.4

Raise

$2$ to the power of

$22$ .

$(\frac{1}{1048576} - \frac{1}{4194304}) \cdot 2^{21}$

Step 3

To write

$\frac{1}{1048576}$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$(\frac{1}{1048576} \cdot \frac{4}{4} - \frac{1}{4194304}) \cdot 2^{21}$

Step 4

Write each expression with a common denominator of

$4194304$ , by multiplying each by an appropriate factor of

$1$ .

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Step 4.1

Multiply

$\frac{1}{1048576}$ by

$\frac{4}{4}$ .

$(\frac{4}{1048576 \cdot 4} - \frac{1}{4194304}) \cdot 2^{21}$

Step 4.2

Multiply

$1048576$ by

$4$ .

$(\frac{4}{4194304} - \frac{1}{4194304}) \cdot 2^{21}$

Step 5

Simplify the expression.

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Step 5.1

Combine the numerators over the common denominator.

$\frac{4 - 1}{4194304} \cdot 2^{21}$

Step 5.2

Subtract

$1$ from

$4$ .

$\frac{3}{4194304} \cdot 2^{21}$

Step 5.3

Raise

$2$ to the power of

$21$ .

$\frac{3}{4194304} \cdot 2097152$

Step 6

Cancel the common factor of

$2097152$ .

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Step 6.1

Factor

$2097152$ out of

$4194304$ .

$\frac{3}{2097152 (2)} \cdot 2097152$

Step 6.2

Cancel the common factor.

$\frac{3}{2097152 \cdot 2} \cdot 2097152$

Step 6.3

Rewrite the expression.

$\frac{3}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$