Question

indicate whether each statement is sometimes, always, or never true.

	sometimes	always	never
$(-0.25)^0 = 1$	$\bigcirc$	$\bigcirc$	$\bigcirc$
$0^0 = 1$	$\bigcirc$	$\bigcirc$	$\bigcirc$
$m^0 = 1$	$\bigcirc$	$\bigcirc$	$\bigcirc$

| $k^0 = 1,\\ k \
eq 0$ | $\bigcirc$ | $\bigcirc$ | $\bigcirc$ |

Explanation:

Step1: Evaluate $(-0.25)^0$

By the zero exponent rule (non-zero base to 0 power is 1): $(-0.25)^0 = 1$. This is always true.

Step2: Evaluate $0^0$

$0^0$ is an indeterminate form, it is not equal to 1. This is never true.

Step3: Evaluate $m^0 = 1$

If $m=0$, $m^0$ is indeterminate; if $m
eq0$, $m^0=1$. So this is sometimes true.

Step4: Evaluate $k^0=1, k

eq0$
By the zero exponent rule, any non-zero base to 0 power is 1. This is always true.

Answer:

1. $(-0.25)^0 = 1$: always
2. $0^0 = 1$: never
3. $m^0 = 1$: sometimes
4. $k^0 = 1, k

eq 0$: always