1.2 What you should learn Why you should learn it Exponents and Powers GOAL 1 Evaluate expressions containing exponents. GOAL 2 Use exponents in real-life applications such as finding the volume of an aquarium. Why you should learn it To solve real-life problems, such as finding the volume of a glass cube.

1.2 Exponents and Powers 1 GOAL EXPRESSIONS CONTAINING EXPONENTS VOCABULARY power base exponent The expression 23 is called a _____. 2 is the _____, and 3 is the _________. The exponent tells you how many times the base is used as a factor. For this example, 23 = 2•2•2. power base exponent Remember:

Extra Example 1 Express the meaning of the power in words and then with numbers or variables. Click for the answers. 81 2. 62 3. 43 4. 97 5. yn 8 to the first power; 8 6 to the second power (or 6 squared); 6•6 4 to the third power (or 4 cubed); 4•4•4 9 to the 7th power; 9•9•9•9•9•9•9 y to the nth power; y•y•y•y•…•yn EXAMPLE 1 EXAMPLE 2

Extra Example 2 Evaluate the expression x4 when x = 3. Click for the solution. Write: x4 Substitute: 34 Simplify: 81 This is what I will expect to see in all of your written work! When an expression contains grouping symbols, remember to perform operations within the innermost set first, then work your way to the outside, always following the order of operations. EXAMPLE 3

Extra Example 3 Evaluate the expression when a = 3 and b = 4. (a + b)3 2. a + (b)3 Click to see the solutions. You may use your calculator once you show your substitution. 1. (a + b)3 (3 + 4)3 73 343 2. a + (b)3 3 + 43 3 + 64 67 Remember: An exponent only applies to the expression immediately on its left. Take a look at EXAMPLE 4

Extra Example 4 Evaluate the expression when x = 5. Click for the solutions. 1. 3x2 2. (3x)2 1. Write Substitute Simplify 2.

Checkpoint Express the meaning of 64 with numbers. Find x5 when x = 4. Evaluate each expression when a = 2 and b = 3. (a + b)2 a2 + b2 Evaluate each expression when x = 2. 4x3 (4x)3 6•6•6•6 1024 13 25 32 512

1.2 Exponents and Powers 2 GOAL REAL-LIFE APPLICATIONS OF EXPONENTS One of the most common applications of exponents is in finding the size of something, either in area or volume. You should know the formula for the area of a square (A = s2) and the volume of a cube (V = s3). Note how to read units of area (ft2 is “square feet”) and units of volume (cm3 is “cubic centimeters”). EXAMPLE 5

Extra Example 5 Make a table showing the area of a square with side lengths 30 cm, 40 cm, 50 cm by using the formula A = s2. Click for a hint, then click again for the solution. Side, s s2 Area 30 cm 40 cm 50 cm 900 900 cm2 1600 1600 cm2 2500 2500 cm2 EXAMPLE 6

Extra Example 6 A tank has the shape of a cube. Each edge is 4.5 feet long. Find the volume in cubic feet. How many gallons of water will the cubic tank hold? (One cubic foot holds 7.48 gallons.) 4.5 ft

Checkpoint Find the total volume of 5 cubes that all have the edge length 3.1 cm. Click for a hint. 3.1 cm V = 5s3 Click for the rest of the solution.

QUESTIONS?