Evaluate (2^-20-2^-22)/(2^-21)

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

Move $2^{- 21}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Simplify each term.

Tap for more steps…

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

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

Raise $2$ to the power of $20$ .

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

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

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

Raise $2$ to the power of $22$ .

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

To write $\frac{1}{1048576}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Write each expression with a common denominator of $4194304$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps…

Multiply $\frac{1}{1048576}$ and $\frac{4}{4}$ .

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

Multiply $1048576$ by $4$ .

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $4$ .

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

Raise $2$ to the power of $21$ .

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

Cancel the common factor of $2097152$ .

Tap for more steps…

Factor $2097152$ out of $4194304$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$

Evaluate (2^-20-2^-22)/(2^-21)

Meet the Team our Math Expers

Our Professionals

Robert Kristofer

Anna Frok

Magnus Flores

Lydia Fran

We are MathExperts

We can solve all your math problems