Evaluate 2^3+3(2)+14÷2

$2^{3} + 3 (2) + 14 \div 2$

Step 1

Find the common denominator.

Write $2^{3}$ as a fraction with denominator $1$ .

$\frac{2^{3}}{1} + 3 (2) + 14 \div 2$

Multiply $\frac{2^{3}}{1}$ by $\frac{2}{2}$ .

$\frac{2^{3}}{1} \cdot \frac{2}{2} + 3 (2) + 14 \div 2$

Multiply $\frac{2^{3}}{1}$ by $\frac{2}{2}$ .

$\frac{2^{3} \cdot 2}{2} + 3 (2) + 14 \div 2$

Write $3 (2)$ as a fraction with denominator $1$ .

$\frac{2^{3} \cdot 2}{2} + \frac{3 (2)}{1} + 14 \div 2$

Multiply $\frac{3 (2)}{1}$ by $\frac{2}{2}$ .

$\frac{2^{3} \cdot 2}{2} + \frac{3 (2)}{1} \cdot \frac{2}{2} + 14 \div 2$

Multiply $\frac{3 (2)}{1}$ by $\frac{2}{2}$ .

$\frac{2^{3} \cdot 2}{2} + \frac{3 (2) \cdot 2}{2} + 14 \div 2$

Step 2

Combine the numerators over the common denominator.

$\frac{2^{3} \cdot 2 + 3 (2) \cdot 2 + 14}{2}$

Step 3

Simplify each term.

Multiply $2^{3}$ by $2$ by adding the exponents.

Multiply $2^{3}$ by $2$ .

Raise $2$ to the power of $1$ .

$\frac{2^{3} \cdot 2^{1} + 3 (2) \cdot 2 + 14}{2}$

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

$\frac{2^{3 + 1} + 3 (2) \cdot 2 + 14}{2}$

Add $3$ and $1$ .

$\frac{2^{4} + 3 (2) \cdot 2 + 14}{2}$

Raise $2$ to the power of $4$ .

$\frac{16 + 3 (2) \cdot 2 + 14}{2}$

Multiply $3 (2) \cdot 2$ .

Multiply $3$ by $2$ .

$\frac{16 + 6 \cdot 2 + 14}{2}$

Multiply $6$ by $2$ .

$\frac{16 + 12 + 14}{2}$

Step 4

Simplify the expression.

Add $16$ and $12$ .

$\frac{28 + 14}{2}$

Add $28$ and $14$ .

$\frac{42}{2}$

Divide $42$ by $2$ .

$21$