Exponents - Which is greatest?

[adi]

Of the following, which is greatest?

A) (1/5) ^ -2
B) (1/3) ^ -2
C) 3^-2
D) 5^-2
E) 2^3

A is the right answer. I thought so too but wasn't exactly sure on the rules. Would you change A to 5^2? If so, what are the exact rules for this one. I know that 3^-2 is (1/3)^2.... would you flip A using the same rule?

[simplyjat]

There is no rule actually, only the definition of negative powers. Negative power n of a number x means 1 divided by x, n times...

[smushkas]

Hey there,

You are right. See, it is a fraction and you have to flip it, too.
(1/5)^-2 = [1 / (1/5)^2] = [1 / (5/1)^2] = [1* 25/1 ] = 25

Hope it is clear!

[xeqtr]

Yes you can flip A using the same rule;
since 1/5 = 5^-1, you end up with (5^-1)^-2 => -1x-2 = 2 =>> 5^2. hope it makes more sense.

Of the following, which is greatest?

A) (1/5) ^ -2
B) (1/3) ^ -2
C) 3^-2
D) 5^-2
E) 2^3

A is the right answer. I thought so too but wasn't exactly sure on the rules. Would you change A to 5^2? If so, what are the exact rules for this one. I know that 3^-2 is (1/3)^2.... would you flip A using the same rule?