Simplify 4/(4^(1/2))

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

Step 1

Move $4^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 2

Multiply $4$ by $4^{- \frac{1}{2}}$ by adding the exponents.

Multiply $4$ by $4^{- \frac{1}{2}}$ .

Raise $4$ to the power of $1$ .

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

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

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

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $2$ .

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

Step 3

Simplify the expression.

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

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

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

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

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$2^{1}$

Step 5

Evaluate the exponent.

$2$