Question

Which expressions are equivalent to 4^-2 * 7^-2

A: (4 * 7)^-4

B: 1/28^2

C: 7^-2 / 4^2

D: (4 * 7)^4

Answer 1

B and C

Explanation:

4^-2 can also be written as 1/4^2 and so can 7^-2

Answer 2

B.
`(1)/(28^2)`

C.
`(7^(-2))/(4^2)`

Explanation:

The given expression is
`4^(-2)*7^(-2)`

We can rewrite in various forms using the rules:
`(a^m)^n=a^(mn)` and
`a^(-m)=(1)/(a^m)`

For instance

`4^(-2)*7^(-2)=(1)/(4^2)*(1)/(7^2)=(1)/((4*7)^2)=(1)/(28^2)`...Option B

OR

`4^(-2)*7^(-2)=(7^(-2))/(4^2)`....Option C

Therefore options B and C are correct