Question

Write the following in exponential form.
a) Square of 3
b) Cube of 51
c) Product of 2 cubed and 3 squared
d) 13 to the power of 9

Answer 1

Hint: We will express the numbers in exponential form, that is as a base raised to a power. The square of a number is the number raised to the power 2. The cube of a number is the number raised to the power 3.

Complete step-by-step answer:
The exponential form of a number is written as \[{a^b}\], where \[a\] is called the base and \[b\] is called the exponent. \[{a^b}\] means \[a\] raised to the power of \[b\], that is \[{a^b} = a \times a \times a \times \ldots \] upto \[b\] times. The number \[{a^b}\] can also be read as the \[{b^{{\text{th}}}}\] power of \[a\].
a) The number \[a\] raised to the power 2 is called the square of \[a\]. The exponential form of the square of a number \[a\] is \[{a^2}\].
Therefore, the exponential form of the square of 3 is \[{3^2}\].
b) The number \[a\] raised to the power 3 is called the cube of \[a\]. The exponential form of the cube of a number \[a\] is \[{a^3}\].
Therefore, the exponential form of the cube of 51 is \[{51^3}\].
d) The number \[a\] raised to the power 3 is called the cube of \[a\]. The exponential form of the cube of a number \[a\] is \[{a^3}\].
Therefore, the exponential form of the cube of 2 is \[{2^3}\].
The number \[a\] raised to the power 2 is called the square of \[a\]. The exponential form of the square of a number \[a\] is \[{a^2}\].
Therefore, the exponential form of the square of 3 is \[{3^2}\].
The product of 2 cubed and 3 squared is the product of \[{2^3}\] and \[{3^2}\].
Product of 2 cubed and 3 squared \[ = {2^3} \times {3^2}\]
e) The exponential form of the \[{b^{{\text{th}}}}\] power of a number \[a\] is \[{a^b}\]. Therefore, the exponential form of 13 to the power of 9 is \[{13^9}\].

Note: In these types of problems, the exponential form of the number should be written as \[{a^b}\], where \[a\] is called the base and \[b\] is called the exponent. It should be taken care that the exponent is not written in the place of the base and the base is not written in the place of the exponent.