Question

Use the order of operations to simplify. (2/7)^2. (7/9)^2 (2/7)^2. (7/9)^2 = (Simplify your answer. Type a whole number or a fraction.)

Answer 1

`(2/7)^(2) (7/9)^(2)(2/7)^(2) (7/9)^(2) = (16)/(6561)`

Explanation:

`(2/7)^(2) (7/9)^(2)(2/7)^(2) (7/9)^(2)`

1. Do what is in parenthesis first. You can distribute the exponent to both the numerator and demonitator of each fraction in order to operate.

`(2^(2) )/(7^(2) ) \frac{7^(2)} {9^(2) } (2^(2) )/(7^(2) ) \frac{7^(2)} {9^(2) }`

2. Exponents (ie Powers and Square Roots, etc.)

`(4)/(49) (49)/(81) (4)/(49) (49)/(81)`

3. Multiplication and Division (left-to-right)

`(4)/(81) (4)/(49) (49)/(81)`

• since multiplication is commutative then :

`(4)/(81) (4)/(49) (49)/(81)` =
`(4)/(49) (49)/(81) (4)/(81)`

• therefore

`(4)/(49) (49)/(81) (4)/(81)` =
`(4)/(81) (4)/(81)`

So:
`(4)/(81) (4)/(81)` =
`(16)/(6561)`