Question

How do you write $400$ in exponential form?

Answer 1

Hint: The exponent of a number is the number to which the base is raised. We know that the number $100$ can be expressed in the exponential form as ${{10}^{2}}.$ Also, remember that $4\times 100=400.$

Complete step by step answer:
Suppose that we have a number of the form ${{a}^{b}}.$ We call $a$ the base and $b$ the exponent.
So, the exponent of a number is the number to which the base is raised. It can also be called the power of the base.
Let us consider the given number, $400.$
We are asked to write $400$ in the exponential form.
We know that if we multiply a number with a hundred, then we will get the product whose leftmost digits are the number and the rightmost digits are the two zeros of a hundred.
We will use this basic rule of multiplication for the further procedure.
So, the given number is $400$ and we know that $400=4\times 100.$
Also, we know that the product of $10$ and $10$ is $100.$ That is, $10\times 10=100.$
We can say that the square of ten is a hundred. That is, ${{10}^{2}}=100.$
If we are using this rule, we will get the exponential form of $400$ as $400=4\times 100=4\times {{10}^{2}}.$

Hence the exponential form of $400$ is $4\times {{10}^{2}}.$

Note: When we say that a quantity increases exponentially, we mean that there is a rapid increase in that quantity. We call this increase the exponential growth. When we say that a quantity decreases exponentially, we mean that there is a rapid decrease in that quantity. We call this decrease the exponential decay.