Evaluate ((2^-1)/(2^0))^3

${(\frac{2^{- 1}}{2^{0}})}^{3}$

Step 1

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

${(\frac{1}{2^{0} \cdot 2})}^{3}$

Step 2

Simplify the denominator.

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

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

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

${(\frac{1}{2^{0} \cdot 2^{1}})}^{3}$

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

${(\frac{1}{2^{0 + 1}})}^{3}$

Add $0$ and $1$ .

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

Simplify $2^{1}$ .

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

Step 3

Apply the product rule to $\frac{1}{2}$ .

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

Step 4

One to any power is one.

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

Step 5

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

$\frac{1}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$