What is an Exponent?

Definition of exponent

An Exponent is a number that states how many times the base number is to be used in multiplication. The Exponent Number appears on the top right of the base number as a small number.

Basic exponent rules

• 5⁵ means 5×5. The smaller number 2 is the Exponent and denotes the number of times 5 needs to be multiplied.
• So instead of writing 2x2x2 we can simply write 2³
• The Exponent way is much shorter and easier to write aⁿ and comes in handy when you need to solve big equations. Exponents are also known as Index or Power.
• Thus we can say that tells you to multiply ‘a’ by itself ‘n’ number of times.

Example: 3⁵ = 3x3x3x3x3= 243

Properties of exponents

Suppose A = 1 or 0 exponent

• If the Exponent is 1 then you have the number itself. Example: = 9¹ = 9
• If the Exponent is 0 then you get 1. Example: 5⁰ = 1
• If both the Number and the Exponent is zero 0⁰ then the result is indeterminate.

Negative Exponents

A Negative Exponent is just the opposite of Multiplication, that is Division.
So, 5^-1
Is basically 1/5² = 1/25= 0.04
A negative exponent means how many times you need to divide 1 by the number.
Example: 6^-3 = 1/= 0.0046

Grouping exponents with signs

In order to avoid confusions, use Parenthesis like () brackets.

There is a difference:

• With brackets: (ab)² = (ab)x(ab)
• Without brackets: ab² = axbxb

Example:

• -2² = (-2)X(-2)= 4
• -2² = -(2)² = -4

Special exponents:

• When a number has an Exponent of 2, it is called Squared.
• When a number has an Exponent of 3, it is called Cubed.

Special cases:

Example : 5² x 5³

• Is same as 5 to the power of 2+3 or 5²
• So when the bases are same you can add the exponents during Multiplication.

Example:

• This is the same as 3 to the power of 4×2 or 3²
• This is the case of exponent on top of an Exponent and here we multiply the Exponents.

Worksheet on exponents

1. Write the expression using exponents:
a) 56 x 56 x 56
b) 1.8×1.8×1.8×1.8×1.8×1.8
c) (-2)x(-2)x(-2)x(-2)

Ans: 56³; 1.8³; -2⁴

2. Solve the following exponents:
a) 10³
b) 0⁴
c) 2⁶
d) 1⁸

Ans: 1000; 0; 64; 1

3. Solve the following equations:
a) -(1/2)⁵
b) -0.5²
c) -1.2³
d) -(5/2)³

Ans: 1/32;  0.25;  1.2;  125/8

4. Solve the equations:
a) 10^-3
b) 3^-2
c) 5^-4
d) 1^-1

Ans: 1/1000;  1/9;  1/625;  1