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

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

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

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

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

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $2$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $2$ .

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

Add $4$ and $1$ .

$4^{\frac{5}{2}}$

Simplify the expression.

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

${(2^{2})}^{\frac{5}{2}}$

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

$2^{2 (\frac{5}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2^{2 (\frac{5}{2})}$

Rewrite the expression.

$2^{5}$

Raise $2$ to the power of $5$ .

$32$