Exponents

What is an exponent? An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 4th power is written like this: 24.

It means 2 x 2 x 2 x 2 = 16

24 is NOT the same as 2 x 4

Examples

31 = 3

32 = 3 × 3 = 9

33 = 3 × 3 × 3 = 27

34 = 3 × 3 × 3 × 3 = 81

35 = 3 × 3 × 3 × 3 × 3 = 243

There are several exponents rules. We will discuss a few of these rules in this post.

Exponents product rules

Product rule with same base

xa ⋅ xb = xa+b

Example:

23 ⋅ 24 = 23+4 = 27 = 2⋅2⋅2⋅2⋅2⋅2⋅2 = 128

Product rule with same exponent

xa ⋅ ya = ( y)a

Example:

32 ⋅ 42 = (3⋅4)2 = 122 = 12⋅12 = 144

Exponents quotient rules

Quotient rule with same base

xa / xb = xab

Example:

25 / 23 = 25-3 = 22 = 2⋅2 = 4

Quotient rule with same exponent

xa / ya = (/ y)a

Example:

43 / 23 = (4/2)3 = 23 = 2⋅2⋅2 = 8

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