Question

(4/9)² ÷ ( 1/3 + 2/9 – ½)

this is an order of operation with exponet problem
please show work and explain how you got the answer

Answer 1

When using the order of operations to solve the problem, then the final answer will be
`(32)/(9)`

Explanation:

`((4)/(9))^2` ÷
`((1)/(3) +(2)/(9) -(1)/(2) )`

Following the order of operations, the first thing we have to do is add 1/3 to 2/9 and then subtract that sum by 1/2.

`((4)/(9))^2` ÷
`((5)/(9) -(1)/(2) )`

`((4)/(9) )^2` ÷
`((1)/(18) )`

Next, we solve the exponent on 4/9 by multiplying 4/9 with itself.

`((4)/(9))^2= (16)/(81)`

`((16)/(81) )` ÷
`((1)/(18) )`

Lastly, we divide 16/81 by 1/18.

`((16)/(81) )` ÷
`((1)/(18) )` =
`(32)/(9)`

Since this number can not be simplified into a smaller fraction, then the answer will stay as it is.

So, your final answer will be
`(32)/(9)`