# Exponentiation

The power notation represents a multiplication of the same number. For example, 2 · 2 · 2 · 2 · 2 = 25

The number that is multiplied is called the base number and the number that expresses the number of multiplications is the exponent. In the notation 25, 2 is the base number and 5 is the exponent (or power).

34 = 3 · 3 · 3 · 3 base 3, exponent 4

42 = 4 · 4 base 4, exponent 2

The product of exponents with the same base.

If we expand 22·23 , we will have 22 ·23 = 2·2·2·2·2 = 25

The short way to do this with same base number is to add the exponents 2x ·2y = 2x+y

The quotient of exponents with the same base.

24 = 2·2·2·2

22 = 2·2

If we expand both exponents, we can reduce the fraction and the final answer is 22

If exponentiation with same base are divided, the exponents are subtracted from each other

Raising the exponentiation by a power.

(23)2 We can expand the exponentiation notation (23)2 = 23 ·23 Product with same base (23)2 = 23 ·23 = 23+3 = 26

The rule is that when the power is raised by a power, the exponents are multiplied. (2x)y = 2x·y

(23)2 = 23·2 = 26

Raising the product by a power.

(2a)2

We can expand the exponentiation notation (2a)2 = 2a·2a

The order of multiplication doesn't matter

2 · 3 = 3 · 2 and 2·3·4 = 4·2·3.

So we rearrange (2a)2 = 2a·2a = 2·2·a·a = 22 ·a2 = 4a2.

All factors from the product must be raised by the power, so (a·b)2 = a2·b2

Raising the quotient by a power.

When the quotient is raised by a power, both the numerator and the denominator are raised by that power.

Negative exponents and an exponent of 0

Turn on the subtitles if needed