Where Should We Start First?

Algebra Level 2

Statement 1. $\large \quad 2^{2^2} = \Big(2^2\Big)^2$

Statement 2. $\large \quad 2^{2^2} = 2^{(2^2)}$

Which of the two statement(s) above is(are) true?

Both statements 1 and 2 Statement 1 only Statement 2 only None of the above is true

2 solutions

Geoff Pilling
Nov 21, 2016

$a^{b^c} = a^{(b^c)}$

However, in general $a^{b^c} \neq (a^b)^c$ .

However, in the example $2^4 = 4^2$ , so it just so happens that for the number Pi chose, $\boxed{\text{both statements are true}}$ .

This just happens to be a special case where the 2 quantities are equal. The rule shoud be assessed not true in my opinion.

Kris Prabhu - 4 years, 6 months ago

Munem Shahriar
Nov 27, 2017

Case 1:

$2^{2^2} = (2^2)^2$

$\Rightarrow 2^4 = 2^{2 \times 2}$

$\Rightarrow 2^4 = 2^4$

$\Rightarrow 16 =16 \longrightarrow \color{#20A900} \text{True}$

Case 2:

$2^{2^2} = 2^{(2^2)}$

$\Rightarrow 2^4 = 2^4$

$\Rightarrow 16 = 16 \longrightarrow \color{#20A900} \text{True}$

Hence both statements 1 and 2 are true.