Evaluate (2^-7*2^6)/(2^0)

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

Step 1

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

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

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

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.

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

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

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

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

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

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

Add $0$ and $1$ .

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

Simplify $2^{1}$ .

$\frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$