Simplify ((2^-4)÷(2^4))÷(2^-5)

$(2^{- 4} \div 2^{4}) \div 2^{- 5}$

Step 1

Rewrite the division as a fraction.

$\frac{2^{- 4} \div 2^{4}}{2^{- 5}}$

Step 2

Move $2^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$2^{- 4} \div 2^{4} \cdot 2^{5}$

Step 3

Combine $2^{- 4} \div 2^{4}$ and $2^{5}$ .

$\frac{2^{- 4} \cdot 2^{5}}{2^{4}}$

Step 4

Multiply $2^{- 4}$ by $2^{5}$ by adding the exponents.

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

$\frac{2^{- 4 + 5}}{2^{4}}$

Add $- 4$ and $5$ .

$\frac{2^{1}}{2^{4}}$

Step 5

Simplify $2^{1}$ .

$\frac{2}{2^{4}}$

Step 6

Cancel the common factor of $2$ and $2^{4}$ .

Factor $2$ out of $2$ .

$\frac{2 (1)}{2^{4}}$

Cancel the common factors.

Factor $2$ out of $2^{4}$ .

$\frac{2 (1)}{2 \cdot 2^{3}}$

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 2^{3}}$

Rewrite the expression.

$\frac{1}{2^{3}}$

Step 7

Raise $2$ to the power of $3$ .

$\frac{1}{8}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$