Question

Evaluate the following expressions:

A. 11^0
B. 11^2

Are the answers to parts a and b the same? Explain why or why not.

Answer 1

Any number (except zero) raised to the power of zero is one:

`11^0=1`

On the other hand, by definition, the square of a number is that number multiplied by itself:

`11^2=11\cdot 11 = 121`

So, the two answer are not the same:

`11^0\\eq 11^2`

After all, the exponential function

`y=11^x`

is injective, which means that, given
`x_1\\eq x_2`, we have

`11^(x_1)\\eq 11^(x_2)`