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What is an Exponent?

Maths | 7-14 yrs | Interactive

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

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