Question

Classify (-7)^2015 as a postive or negative integer (show work)

Answer 1

We can classify numbers elevated to an exponent as positive or negative depending on whether the exponent is an odd number or an even number.

When the number we have is a negative number, and we elevate that number to an exponent that is an even number, the result will be a positive number. For example:

$(-2)^2=4$

And when the number we have is a negative number (such as the case of -7) and we elevate that number to an exponent that is an odd number (such as the case of 2015), the result will be a negative number.

We can explain this result using smaller numbers, for example:

$(-2)^3$

We can express this as a multiplication of three times -2:

$(-2)^3=(-2)(-2)(-2)$

And the result will be negative:

$\begin{gathered} (-2)^3=(+4)(-2) \\ (-2)^3=-8 \end{gathered}$

This will always be the case when we have a negative number elevated to an odd power.

Answer: (-7)^2015 is a negative number because the exponent is an odd number.