Evaluate (5(16)^(1/4))/4

$\frac{5 {(16)}^{\frac{1}{4}}}{4}$

Step 1

Simplify the numerator.

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

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 2

Reduce the expression by cancelling the common factors.

Multiply $5$ by $2$ .

$\frac{10}{4}$

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$\frac{2 (5)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{2 \cdot 5}{2 \cdot 2}$

Cancel the common factor.

$\frac{2 \cdot 5}{2 \cdot 2}$

Rewrite the expression.

$\frac{5}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$