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How do you simplify ${5^0}$ ?

Last updated date: 26th Feb 2024
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IVSAT 2024
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Hint: There are a large variety of functions in mathematics and they all have an important role. One such function is the exponential function, exponential functions are those functions in which one term is raised to the power of another term. The power indicates the number of times the base term is multiplied with itself. Let an exponential function be ${a^n}$ , where “a” is the base and “n” is the power, 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 ${5^0}$ .

Complete step by step solution:
We know that ${a^0} = 1$
In this question $a = 5$ , so we get –
${5^0} = 1$
Hence, the simplified form of ${5^0}$ 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.