Question

natalie tried to evaluate the expression \\(\left(4^{-3} \cdot 2^{-3}\
ight)^0\\).
\\(\

$$\begin{align*} \\left(4^{-3} \\cdot 2^{-3}\ ight)^0&= \\left(8^{-3}\ ight)^0 & \\text{step 1} &= 8^0 & \\text{step 2} &= 0 & \\text{step 3} \\end{align*}$$

did natalie make a mistake? if so, in which step?
choose 1 answer:
\\(\boldsymbol{\text{a}}\\) natalie did not make a mistake.
\\(\boldsymbol{\text{b}}\\) natalie made a mistake in step 1.
\\(\boldsymbol{\text{c}}\\) natalie made a mistake in step 2
\\(\boldsymbol{\text{d}}\\) natalie made a mistake in step 3.

Explanation:

Step1: Check Step 1 validity

$4^{-3} \cdot 2^{-3} = (4 \cdot 2)^{-3} = 8^{-3}$. This step is correct.

Step2: Check Step 2 validity

$(8^{-3})^0 = 8^{-3 \cdot 0} = 8^0$. This step is correct.

Step3: Check Step 3 validity

Any non-zero number to the power of 0 is 1, so $8^0 = 1$, not 0. This step is wrong.

Answer:

D. Natalie made a mistake in Step 3.