Which of the following is equivalent to (-3)^-3?

A. 9
B. 1/27
C. -9
D1/-27

When we have a negative exponent, we use the negative exponent property: a negative exponent with it’s base must be the reciprocal of the base and negative exponent, in order to make it a positive exponent.

Solving:

(-3)^-3/1

We made the base of -3 and exponent of -3 a fraction over 1, because we will need to take the reciprocal (flipped upside down fraction) of it.

1/(-3)^3

We now have a positive exponent. We took the reciprocal of (-3)^-3/1, so we just flipped the fraction upside down to 1/(-3)^3, which gave us a positive exponent.

1/(-3)^3 = 1/(-3)(-3)(-3) by the definition of an exponent (how many times a number multiplies itself).

Now , we just simply by multiplying -3 to itself 3 times.

1/-27 is the answer.