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:

$11^0\neq 11^2$

After all, the exponential function

$y=11^x$

is injective, which means that, given $x_1\neq x_2$, we have

$11^{x_1}\neq 11^{x_2}$