We know how to calculate the expression 5 x 5. This expression
can be written in a shorter way using something called
exponents.
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.
3^{1}

3 to the first power

3

4^{2}

4 to the second power or 4
squared

4 ∙ 4

5^{3}

5 to the third power or 5
cubed

5 ∙ 5 ∙ 5

2^{6}

2 to the power of six

2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2

Example:
Write these multiplications like exponents
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:
Example:
Division: If two powers have the same base then we can divide
the powers. When we divide powers we subtract their exponents.
The rule:
Example:
A negative exponent is the same as the reciprocal of the
positive exponent.
Example:
When you raise a product to a power you raise each factor with a
power
Example:
The rule for the power of a power and the power of a product can
be combined into the following rule:
Example:
Video lesson: Rewrite the expressions
Video lesson: Simplify the expression