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

x^a ⋅ x^b = x^a+b

Example:

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

Product rule with same exponent

x^a ⋅ y^a = (x ⋅ y)^a

Example:

3² ⋅ 4² = (3⋅4)² = 12² = 12⋅12 = 144

Exponents quotient rules

Quotient rule with same base

x^a / x^b = x^a–b

Example:

2⁵ / 2³ = 2^5-3 = 2² = 2⋅2 = 4

Quotient rule with same exponent

x^a / y^a = (x / y)^a

Example:

4³ / 2³ = (4/2)³ = 2³ = 2⋅2⋅2 = 8

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