Question

Is the following statement always, never, or sometimes true?

A number raised to a negative exponent is negative.

always
never**
sometimes

Answer 1

The answer is sometimes

Answer 2

We need to complete the statement that " A number raised to a negative exponent is ___ negative"

Consider a number 'a' raised to a negative exponent say '-m'.

$a^{-m}$

According to the law of exponents.

We get, $a^{-m}=\frac{1}{a^{m}}$

Now let us consider two cases:

Case 1 : If 'a' is a positive number, let a = 'x'.

Then, $a^{-m}=x^{-m=}\frac{1}{x^{m}}$ which is positive.

Case 2: If 'a' is a negative number, let a= '-x '

Then, $a^{-m}=(-x)^{-m=}\frac{1}{-x^{m}}$ which is negative.

Therefore, we can say that

" A number raised to a negative exponent is sometimes negative".