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?

Given:

The expression is

[tex]\left( 4^{-3} \cdot 2^{-3} \right)^{0} [/tex]

To find:

The Natalie's mistake.

Solution:

We have,

[tex]\left( 4^{-3} \cdot 2^{-3} \right)^{0} [/tex]

Using properties of exponents, we get

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

[tex]=\left( (8)^{-3} \right)^{0}[/tex]

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

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

Therefore, Natalie make a mistake in Step 3. She write [tex]8^0=0[/tex] instead of [tex]8^0=1[/tex].

Answer:

d

Step-by-step explanation:

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