Question

How do you simplify ${2^0}$ ?

Answer 1

In mathematics, there are a large variety of functions and they all have an important role. An exponential function is one such function; exponential functions are those functions in which one term is raised to the power of another term. Let an exponential function be ${a^n}$ , where “a” is the base and “n” is the power; the power indicates the number of times the base term is multiplied with itself, so it can be written as “a” multiplied by itself n times and thus its value can be obtained very easily. Similarly, we can find the value of ${2^0}$ .

Complete step-by-step solution:
We know that ${a^0} = 1$
In this question $a = 2$ , so we get –
${2^0} = 1$
Hence, the simplified form of ${2^0}$ is 1.

Note: ${a^0}$ signifies that a is multiplied with itself zero items. We know that any number except 0 multiplied with 1 is that number itself, so we can write ${a^0}$ as $1 \times {a^0}$ , as a is multiplied with itself zero times so a doesn’t really exist in the expression and thus ${a^0} = 1$ . Students often get confused that ${0^1} = 0$ while ${0^0} = 1$ , now ${0^0}$ can be written as $1 \times {0^0}$ , as 0 is raised to the power 0, so 0 doesn’t really exist and the answer is 1, but ${0^1}$ means 0 multiplied with itself 1 time so the answer is also 0. Even if we write ${0^1}$ as $1 \times {0^1}$ , we will get $1 \times 0$ and we know that any number multiplied with zero gives 0 as the answer, thus the answer still comes out to be zero.