Algebra Examples

$2^{- 7} \cdot \frac{2^{- 7}}{2^{0}}$

Step 1

Simplify the numerator.

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Step 1.1

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

$2^{- 7} \cdot \frac{\frac{1}{2^{7}}}{2^{0}}$

Step 1.2

Raise $2$ to the power of $7$ .

$2^{- 7} \cdot \frac{\frac{1}{128}}{2^{0}}$

Step 2

Anything raised to $0$ is $1$ .

$2^{- 7} \cdot \frac{\frac{1}{128}}{1}$

Step 3

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

$\frac{1}{2^{7}} \cdot \frac{\frac{1}{128}}{1}$

Step 4

Combine.

$\frac{1 (\frac{1}{128})}{2^{7} \cdot 1}$

Step 5

Cancel the common factor of $1$ .

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Step 5.1

Cancel the common factor.

$\frac{1 (\frac{1}{128})}{2^{7} \cdot 1}$

Step 5.2

Rewrite the expression.

$\frac{\frac{1}{128}}{2^{7}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{128} \cdot \frac{1}{2^{7}}$

Step 7

Combine fractions.

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Step 7.1

Combine.

$\frac{1 \cdot 1}{128 \cdot 2^{7}}$

Step 7.2

Multiply $1$ by $1$ .

$\frac{1}{128 \cdot 2^{7}}$

Step 8

Simplify the denominator.

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Step 8.1

Rewrite $128$ as $2^{7}$ .

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

Step 8.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{2^{7 + 7}}$

Step 8.3

Add $7$ and $7$ .

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

Step 9

Raise $2$ to the power of $14$ .

$\frac{1}{16384}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{16384}$

Decimal Form:

$6.10351562 \cdot 10^{- 5}$