Evaluate 16^(1/2)*2^-3

$16^{\frac{1}{2}} \cdot 2^{- 3}$

Step 1

Simplify the expression.

Rewrite $16$ as $4^{2}$ .

${(4^{2})}^{\frac{1}{2}} \cdot 2^{- 3}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4^{2 (\frac{1}{2})} \cdot 2^{- 3}$

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

$4^{2 (\frac{1}{2})} \cdot 2^{- 3}$

Rewrite the expression.

$4^{1} \cdot 2^{- 3}$

Step 3

Evaluate the exponent.

$4 \cdot 2^{- 3}$

Step 4

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

$4 \cdot \frac{1}{2^{3}}$

Step 5

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

$4 \cdot \frac{1}{8}$

Step 6

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$