Simplify ((4^(5/4)*4^(1/4))/(4^(1/2)))^(1/2)

${(\frac{4^{\frac{5}{4}} \cdot 4^{\frac{1}{4}}}{4^{\frac{1}{2}}})}^{\frac{1}{2}}$

Multiply $4^{\frac{5}{4}}$ by $4^{\frac{1}{4}}$ by adding the exponents.

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

${(\frac{4^{\frac{5}{4} + \frac{1}{4}}}{4^{\frac{1}{2}}})}^{\frac{1}{2}}$

Combine the numerators over the common denominator.

${(\frac{4^{\frac{5 + 1}{4}}}{4^{\frac{1}{2}}})}^{\frac{1}{2}}$

Add $5$ and $1$ .

${(\frac{4^{\frac{6}{4}}}{4^{\frac{1}{2}}})}^{\frac{1}{2}}$

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Multiply $4^{\frac{3}{2}}$ by $4^{- \frac{1}{2}}$ by adding the exponents.

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

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $3$ .

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

Divide $2$ by $2$ .

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

Simplify the expression.

Simplify $4^{1}$ .

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$2^{1}$

Evaluate the exponent.

$2$