The mass of the moon is 7,350,000,000,000,000,000,000,000 kg. Can you read this number? It’s not so easy to read or even recognize all these long digits accurately. Therefore in order to give a precise evaluation of the mass of moon we can use Exponents.

Before going into the concept of exponents let us recall about Natural Numbers. In mathematics, natural numbers are defined as the number which are a set of all counting numbers starting from \(1\). The natural number includes all the positive Integers (from 0 to \(\infty\)). Fractional numbers are not a part of natural numbers.

Talking about the concept of Exponents, it is defined as the number which represent the large numbers like mass of moon (as shown above) in shorter form. In exponents, the following two specialized names are available.

1. \(10^2\) = “\(10\) raised to the power of \(2\)” or “\(10\) squared”

2. \(10^3\) = “\(10\) raised to the power of \(3\)” or “\(10\) cubed”

**Example1 :**\(1,000\) = \(10 ~\times ~10 ~\times ~10\) = \(10^3\)

In the above example, \(10^3\) indicate the result for the source \(10 ~\times~ 10~ \times~ 10\). In \(10^3\), \(10\) is the base and \(3\) is the exponent. \(10^3\) can be read as “\(10\) rose to the power of \(3\)” or “\(10\) cubed”. The exponential form of \(1000\) is \(10^3\).

**Example 2 : Write the exponential form of 8.
**

**Solution:**

In the above example, the exponential form of \(8\) is \(2^3\).

Exponents are used to write the numbers in an expanded form. The following example will give better understanding to write a number in an expanded form.

\(12345\) = \(1 ~\times~ 10000~ +~ 2 ~\times~ 1000~ +~ 3~ \times ~100~ +~ 4~ \times~ 10~ +~ 5~\times~ 1\)

= \(1~ \times~ 104~ +~ 2 ~\times ~103~ +~ 3 ~\times ~102 ~+ ~4 ~\times ~10 ~+ ~5\)

**Example 3: What is the exponential form of \(128\)? Mention its base and exponent.**

**Solution:** \(128\) = \(2~ \times~ 2~ \times~ 2~\times~ 2~ \times~ 2~ \times~ 2~\times~ 2 \) = \(2^{7}\)

In the above example, “\(2\)” is the base which is in seven times repeated multiplication, equals “\(128\)”. So, the base is \(2\) and the exponent is \(7\).

**Example 4: Which one is smaller \(4^{2}\) or \(2^{5}\)?**

** Solution:
**\(4^{2}\) = \(4 ~\times~ 4\) = \(16\)

\(2^{5}\) = \(2~ \times~ 2~ \times~ 2 ~\times~2 ~\times~ 2\) = \(32\)

Therefore, \(4^{2} < 2^{5}\)

We have thus seen this basic introduction and examples of the exponents of natural numbers. For the complete understanding of the topic visit our site or download the Byju’s-The learning app.