# How do you evaluate (1+ 3^ { 2} ) \div 2\cdot 3^ { 2}?

Dec 13, 2017

45

#### Explanation:

You would want to follow the order of operations BEDMAS (Bracket, exponent, division, multiplication, addition, subtraction.)

Let's start by solving what's in the brackets, so

(1+3^2)÷2*3^2

= (1+9)÷2*3^2

(10)÷2*3^2

Next, we can solve for the exponents

(10)÷2*3^2

= 10÷2*9

Since we see the division prior to the multiplication, we have to solve that portion first.

 10÷2*9

$= 5 \cdot 9$

Now all we have left is to multiply.

$5 \cdot 9$

$= 45$

Dec 13, 2017

$\frac{5}{9}$

#### Explanation:

$= \frac{1 + {3}^{2}}{2 \cdot {3}^{2}}$

$= \frac{1}{2 \cdot {3}^{2}} + {3}^{2} / \left(2 \cdot {3}^{2}\right)$

$= \frac{1}{2 \cdot {3}^{2}} + \frac{1}{2}$

$= \left(\frac{1}{2}\right) \cdot \left(\frac{1}{3} ^ 2 + 1\right)$

$= \left(\frac{1}{2}\right) \cdot \left(\frac{1}{9} + 1\right)$

$= \left(\frac{1}{2}\right) \cdot \left(\frac{1 + 9}{9}\right)$

$= \frac{10}{2 \cdot 9}$

$= \frac{5}{9}$