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 = (x ⋅ y)a
Example:
32 ⋅ 42 = (3⋅4)2 = 122 = 12⋅12 = 144
Exponents quotient rules
Quotient rule with same base
xa / xb = xa–b
Example:
25 / 23 = 25-3 = 22 = 2⋅2 = 4
Quotient rule with same exponent
xa / ya = (x / y)a
Example:
43 / 23 = (4/2)3 = 23 = 2⋅2⋅2 = 8
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