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Algebra Level 2

We know that for all positive integers $X$ , the following equation is true.

$2^X = \underbrace{2\times 2\times 2\times \cdots \times 2}_{\text{Number of 2's } =X}$

What number goes into the following box such that the equation below is also true for all positive integers $X$ ?

$\boxed{\phantom0}^X = \underbrace{2\times 2\times 2\times \cdots \times 2}_{\text{Number of 2's } =4X}$

16 8 32 4

2 solutions

Edwin Gray
Jan 11, 2019

(2^4)^x = 2^(4x). Ed Gray

Achal Jain
Feb 27, 2017

Note that

$\underbrace{ 2\times 2\times\ 2\times \cdots \times 2}_{ \text{ Number's of 2's=4x} }$ $=$ $2^{4X}$ $=$ $\large {16}^X$

The solution is spot on, but I have to say... the LaTeX gods may strike you down for breaking up the equation like that (~_^)

Brian Moehring - 4 years, 3 months ago