1.2 Exponents and Powers

An expression like is called a power. The exponent 3 represents the number of times the base 2 is used as a factor.

32

32

base onentexp

222

ExamplesExponential Exponential

FormFormWordsWords MeaningMeaning

four to the second four to the second power or four power or four squaredsquared

Five to the third Five to the third power or five power or five cubedcubed

X to the sixth X to the sixth powerpower

24356x

44

555

xxxxxx

Practice

A. 3 squared

B. x to the fourth power

C. s cubed

Evaluate the Power

Evaluate when x = 2

= = 16

4x

44 2x2222

Grouping Symbols

- Indicate the order in which the operations should be performed.

- Operations within the innermost set of grouping symbols are done first

- ( ) parentheses- [ ] brackets

Evaluate Exponents a = 1 and b = 2

A.

5

)()( 22 ba )2()1( 22 )22()11(

41

Practice

a = 1 b = 2

B. (a + b) 2

Exponents and Grouping

x = 4

A. B. 32x 3)2( x

Real-Life Applications

Exponents are often used in the formulas for area and volume.

Squared and CubedArea and Volume

Finding Volume

An aquarium has the shape of a cube.Each edge is 2.5 feet long.

a. Find the volume in cubic feet.b.How many gallons of water will the cubic

aquarium hold? Convert to liquid volume, where one cubic foot holds 7.48 gallons.