Answer:

We know how to calculate the expression 5 x 5. This expression can be written in a shorter way using something called exponents.

5⋅5=52

An expression that REPRESENTS repeated MULTIPLICATION of the same factor is called a power.

The number 5 is called the base, and the number 2 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.

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31 3 to the FIRST power 3

42 4 to the second power or 4 squared 4 ∙ 4

53 5 to the third power or 5 cubed 5 ∙ 5 ∙ 5

26 2 to the power of six 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2

Example

Write these multiplications like exponents

5⋅5⋅5=53

4⋅4⋅4⋅4⋅4=45

3⋅3⋅3⋅3=34

Multiplication

If TWO powers have the same base then we can multiply the powers. When we multiply two powers we add their exponents.

The rule:

xa⋅xb=xa+b

Example

42⋅45=(4⋅4)⋅(4⋅4⋅4⋅4⋅4)=47=42+5

Division

If two powers have the same base then we can divide the powers. When we divide powers we subtract their exponents.

The rule:

xaxb=xa−b

Example

4245=⧸4⋅⧸4⧸4⋅⧸4⋅4⋅4⋅4=143=4−3=42−5

A negative exponent is the same as the reciprocal of the positive exponent.

x−a=1xa

Example

2−3=123

When you raise a PRODUCT to a power you raise each factor with a power

(x⋅y)a=xa⋅ya

Example

(2x)4=24⋅x4=16x4

The rule for the power of a power and the power of a product can be combined into the following rule:

(xa⋅yb)z=xa⋅z⋅yb⋅z

Example

(x3⋅y4)2=x3⋅2⋅y4⋅2=x6⋅y8