Question

How do you simplify `(\frac{2}{a^{2}})^{2}`?

Answer 1

`4/a^4`

Explanation:

= `(2/a^2)^2`

= `2/a^2*2/a^2`

= `4/a^4`

Answer 2

See a solution process below:

Explanation:

First, use this rule of exponents to rewrite the numerator:

`c = c^color(red)(1)`

`(2/a^2)^2 = (2^color(red)(1)/a^2)^2`

Now, use this rule of exponents to complete the simplification:

`(x^color(red)(j))^color(blue)(k) = x^(color(red)(j) xx color(blue)(k))`

`(2^color(red)(1)/a^color(red)(2))^color(blue)(2) => 2^(color(red)(1)xxcolor(blue)(2))/a^(color(red)(2)xxcolor(blue)(2)) => 2^2/a^4 = 4/a^4`