Partielo | Exponents

Définition

Base

is the number which is use for the multiplication when using an exponent. In a number 10³, 10 is the base.

Index (indices)

is the power or exponent which is raised to a number or a variable. Example, in number 2,³3 is the index of 2.

Power (puissance)

power is referred to the number of times a number is multiplied by itself meaning the number you get raising a number to an exponent.

EX: Base,Power,Index

Index form

We know that:

So, we can write 8 as 2³.

Likewise, 27 can be written as 3³

and 125 can be written as 5³.

So far, we have considered numbers that have a group of the same factors. Sometimes, a number has more than one group of the same factors as shown in the following example.

Example 20

Write 200 in simplest index form.

Solution:

In index form, 200 is 2 cubed times 5 squared

Small numbers

can also be written in standard form. However, instead of the index being positive (in the above example, the index was 3), it will be negative. The rules when writing a number in standard form is that first you write down a number between 1 and 10, then you write × 10(to the power of a number).

Big numbers

??103 = 1000, so 4 × 103 = 4000 . So 4000 can be written as 4 × 10³ . This idea can be used to write even larger numbers down easily in standard form.