Evaluate (24^2-8÷2)/((5+2)2)

$\frac{2 \cdot 4^{2} - 8 \div 2}{(5 + 2) \cdot 2}$

Step 1

Reduce the expression by cancelling the common factors.

Cancel the common factor of $8$ and $2$ .

Factor $2$ out of $8$ .

$\frac{2 \cdot 4^{2} - 2 \cdot 4 \div 2}{(5 + 2) \cdot 2}$

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $4$ by $1$ .

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

Cancel the common factor of $2 \cdot 4^{2} - 1 \cdot 4$ and $2$ .

Factor $2$ out of $2 \cdot 4^{2}$ .

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

Factor $2$ out of $- 1 \cdot 4$ .

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

Factor $2$ out of $2 (4^{2}) + 2 (- 1 \cdot 2)$ .

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

Cancel the common factors.

Factor $2$ out of $(5 + 2) \cdot 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Simplify the numerator.

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

$\frac{16 - 1 \cdot 2}{5 + 2}$

Multiply $- 1$ by $2$ .

$\frac{16 - 2}{5 + 2}$

Subtract $2$ from $16$ .

$\frac{14}{5 + 2}$

Step 3

Simplify the expression.

Add $5$ and $2$ .

$\frac{14}{7}$

Divide $14$ by $7$ .

$2$

Evaluate (2*4^2-8÷2)/((5+2)*2)