Algebra Examples

$\frac{2^{- 7} \cdot 2^{6}}{2^{0}}$

Step 1

Multiply $2^{- 7}$ by $2^{6}$ by adding the exponents.

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Step 1.1

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

$\frac{2^{- 7 + 6}}{2^{0}}$

Step 1.2

Add $- 7$ and $6$ .

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

Step 2

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

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

Step 3

Simplify the denominator.

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Step 3.1

Multiply $2^{0}$ by $2$ by adding the exponents.

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Step 3.1.1

Multiply $2^{0}$ by $2$ .

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Step 3.1.1.1

Raise $2$ to the power of $1$ .

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

Step 3.1.1.2

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

$\frac{1}{2^{0 + 1}}$

Step 3.1.2

Add $0$ and $1$ .

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

Step 3.2

Simplify $2^{1}$ .

$\frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$