Question

A negative number raised to an odd power ______ negative

Answer 1

A negative number raised to an odd power IS negative

Answer 2

Answer:

A negative number raised to an odd power is always negative.

Step-by-step explanation:

To complete the statement - A negative number raised to an odd power ______ negative.

Solution :

We know that,

A negative number raised to an odd power is always negative.

1) When a negative number is raised to an even power, the pairs of negatives will cancel out.

For example - $(-1)^2=(-1)\times (-1)=1$

2) When it is raised to an odd power, after pairs of the negative sign have canceled each other out, there will still be one minus sign left unpaired, which will not cancel out.

For example - $(-1)^3=(-1)\times (-1)\times (-1)=1\times (-1)=-1$

Therefore, The required blank is 'always'.