Lesson 7. Exponentiation

вторник, 8 ноября 2016 г.

In the expression x^a the quantity x is called the base, a is the exponent of the power, and x^a is the ath power of a or x raised to the ath power.

EXAMPLE:

The exponents of the quantities 6³ 2⁴ 5⁵ and 3² are, respectively, 3, 4, 5 and 2.

Square number

When a whole number is multiplied by itself, we get a square number.

EXAMPLE:

3 × 3 = 9

We write this as 3² (3 squared)

3²= 3 × 3 = 9

5²= 5 × 5 = 25

Cube number

When a whole number is multiplied by itself 3 times, we get a cube number.

EXAMPLE:

2 × 2 × 2 = 8

We write this as 2³ (2 squared)

1³= 1 × 1 × 1 = 1

(This is 1 cubed. Sometimes we say 1 to the power 3)

EXAMPLES:

3 × 3 is written as 3²

(power 2)

3 × 3 × 3 is written as 3³

(power 3)

3 × 3 × 3 × 3 is written as 3⁴

(the power 4 means multiply 4 lots of 3 together)

For 3⁴ we say ‘3 to the power 4’

‘3 to the power 5’ is 3⁵ which means

3 × 3 × 3 × 3 × 3

Numbers written using powers are said to be in index form

EXAMPLES:

81 written index form is 3⁴

(because 3 × 3 × 3 × 3 × 3 = 81)

20 written index form is 2² × 5

(because 2 × 2 × 5 = 20)

Tasks to the lesson 7

Other lessons:

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вторник, 8 ноября 2016 г.