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

d

Explanation:

Answer 2

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* 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`.