Evaluate 1/(2(4)^(1/2))

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

Step 1

Simplify the denominator.

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

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

Multiply the exponents in ${(2^{2})}^{\frac{1}{2}}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Add $1$ and $1$ .

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

Step 2

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

$\frac{1}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$