Exponents

Exponents

 

Exponents are an abbriviation for a multiplication of the same factors. You multiply the same factors und write this down, using an exponent. The exponent symbolizes the numbers of the same factors. This is very practical with long figures.

 

I’ll show this by an example:

 

Short writing with an exponent

 

            [image]

 

The exponent 4 shows that 4 factors are involved. In this example the same factor is 5.

 

Compare the long writing (very copious):

 

            5 times 5 times 5 times 5 times 5 = 625

 

 

[image]  Definition of exponentation

 

Exponentiation is the product of n factors, each of which is equal to b. The product of exponentiation can also be called power.

 

 

 

Baseexponent = power

 

[image]

 

b = base, n = exponent. Speak: b raised to the power of n.

 

 

Often you hear b2 as b squared and b3 as b cubed. This is because of the plane of a square [image] and the volume of a cube [image].

 

The exponents here show the dimensions. The exponent 2 indicates the regular plane of a square with two dimensions. The exponent 3 indicates the regular volume of a cube with three dimensions. The side-length b is equal.

 

To take an exponent is very practical in physics. Image the big numbers. You can easily substitute the many 0 by an exponent.

 

1,000 = 103    (n = 3, three 0)

 

1,000,000 = 106          (n = 6, six 0)

 

10100    (n = 100, one hundred 0). This number is called googol. The enterprise Google overtook this name, to demonstrate its target of collection a plenty of informations.

 

 

[image] Example 1

 

 

Evaluate the following:

 

 [image]

 

You first multiply the numbers with the exponent and then sum the products.

 

 

[image] Example 2

 

Simplify the expression:

 

 [image]

 

You order the terms and then evaluate them. A cube (volume) cannot be summed up with a line (length). The dimensions are different. So you must add them separately.