Question

Natalie tried to evaluate the expression \left( 4^{-3} \cdot 2^{-3} \right)^{0}(4 −3 ⋅2 −3 ) 0 left parenthesis, 4, start superscript, minus, 3, end superscript, dot, 2, start superscript, minus, 3, end superscript, right parenthesis, start superscript, 0, end superscript. \begin{aligned} &\phantom{=}\left( 4^{-3} \cdot 2^{-3} \right)^{0} \\\\ &=\left( 8^{-3}\right)^{0} &\text{Step } 1 \\\\ &= 8^{0} &\text{Step } 2 \\\\ &=0&\text{Step } 3 \end{aligned} ​ =(4 −3 ⋅2 −3 ) 0 =(8 −3 ) 0 =8 0 =0 ​ Step 1 Step 2 Step 3 ​ Did Natalie make a mistake? If so, in which step?

Answer 1

Given:

The expression is

$\left( 4^{-3} \cdot 2^{-3} \right)^{0}$

To find:

The Natalie's mistake.

Solution:

We have,

$\left( 4^{-3} \cdot 2^{-3} \right)^{0}$

Using properties of exponents, we get

$=\left( (4\times 2)^{-3} \right)^{0}$       $[\because a^mb^m=(ab)^m]$

$=\left( (8)^{-3} \right)^{0}$

$=\left( 8 \right)^{0}$               $[\because (a^m)^n=a^{mn}]$

$=1$                 $[\because a^0=1,\text{ where, a is any non zero number}]$

Therefore, Natalie make a mistake in Step 3. She write $8^0=0$ instead of $8^0=1$.

Answer 2

Answer:

d

Step-by-step explanation: