Question

When an exponent of a power is an even number and the base is a negative number, the value is always:

A. positive
B. negative
C. 0
D. none of the choices

Answer 1

Answer: A. positive

Explanation:

We know that powers are written in this form:

`b^m`

Where "b" is the base and "m" is the exponent.

By definition, the exponent indicates how many times to base must be multiplied by itself. Then, if the base is negative and the exponent is an even number, you get:

`(-3)^4=(-3)(-3)(-3)(-3)=81\\\\\\(-2)^2=(-2)(-2)=2\\\\\\(-5)^6=(-5)(-5)(-5)(-5)(-5)(-5)=15,625`

Therefore, when an exponent of a power is an even number and the base is a negative number, the value is always positive.

Answer 2

The correct answer option is A. positive.

Explanation:

When an exponent or a power is an even number and the base is a negative number, the value is always positive.

Suppose we have a negative base
`- 3` and a power which is even, lets say,
`6` so what we get is a positive value.

`(-3)^6=729`

Therefore, a negative base with even power is always a positive value.