1.1 Evaluate Expressions You will evaluate algebraic expressions and use exponents Essential Question: How do you evaluate algebraic expressions and powers?

Evaluate algebraic expressions EXAMPLE 1 Evaluate algebraic expressions Evaluate the expression when n = 3. a. 13 n = 13 3 Substitute 3 for n. = 39 Multiply. b. 9 n 9 3 = Substitute 3 for n. = 3 Divide. c. n – 1 = 3 – 1 Substitute 3 for n. = 2 Subtract. d. n + 8 = 3 + 8 Substitute 3 for n. = 11 Add. 2

Evaluate the expression when y = 2. GUIDED PRACTICE for Example 1 Evaluate the expression when y = 2. 1. 6y = 12 2. 8 y = 4 3. y + 4 = 6 4. 11 – y = 9 3

EXAMPLE 2 Evaluate an expression Movies The total cost of seeing a movie at a theater can be represented by the expression a + r where a is the cost (in dollars) of admission and r is the cost (in dollars) of refreshments. Suppose you pay $7.50 for admission and $7.25 for refreshments. Find the total cost.

Evaluate an expression EXAMPLE 2 Evaluate an expression SOLUTION Total cost = a + r Write expression. = 7.50 + 7.25 Substitute 7.50 for a and 7.25 for r. = 14.75 Add. The total cost is $14.75 ANSWER

EXAMPLE 3 Read and write powers Write the power in words and as a product. Product Words Power a. 71 seven to the first power 7 b. 52 five to the second power, or five squared 5 5 c. 1 3 2 1 2 one half to the third power, or one half cubed d. z5 z to the fifth power z z z z z

GUIDED PRACTICE for Examples 2 and 3 5. WHAT IF? In Example 2, suppose you go back to the theater with a friend to see an afternoon movie. You pay for both admissions.Your total cost (in dollars) can be represented by the expression 2a. If each admission costs $4.75, what is your total cost? The total cost is $9.50. ANSWER

GUIDED PRACTICE for Examples 2 and 3 Write the power in words and as a product. Product Words Power 6. 95 Nine to the fifth power 9 9 9 9 9 7. 28 Two to the eighth power 2 2 2 2 2 2 2 2 8. n4 n to the fourth power n n n n

EXAMPLE 4 Evaluate powers Evaluate the expression. a. x4 when x = 2 b. n3 when n = 1.5 SOLUTION a. x4 = 24 b. n3 = 1.53 = 2 2 2 2 = (1.5)(1.5)(1.5) = 16 = 3.375

GUIDED PRACTICE for Example 4 Evaluate the expression. 9. x3 when x = 8 10. k3 when k = 2.5 ANSWER 9. 512 10. 6.25

GUIDED PRACTICE for Example 4 Evaluate the expression. 11. d4 when d = 1 3 ANSWER 11. 1 81

The volume of the storage cube is 2744 cubic inches. EXAMPLE 5 Evaluate a power Storage cubes Each edge of the medium-sized pop-up storage cube shown is 14 inches long. The storage cube is made so that it can be folded flat when not in use. Find the volume of the storage cube. SOLUTION V = s3 Write formula for volume. = 143 Substitute 14 for s. = 2744 Evaluate power. The volume of the storage cube is 2744 cubic inches. 12

The area of the square is 196 in2. ANSWER GUIDED PRACTICE for Example 5 WHAT IF? In Example 5, suppose the storage cube is folded flat to form a square. Find the area of the square. The area of the square is 196 in2. ANSWER 13

Evaluate the expression or power. Daily Homework Quiz Evaluate the expression or power. 1. 13g when g = 7 ANSWER 91 2. 1.65 – a when a = 0.75 ANSWER 0.9 3. 54 ANSWER 625 14

Daily Homework Quiz 1 4. 3 1 ANSWER 27 5. Emily is saving for a $300 bicycle. She has saved $128.25. The amount she still needs to save is given by the expression c – s, where c is the cost of the bicycle and s is the amount she has saved. How much does she have left to save? 5. $171.75 ANSWER 15

You will evaluate algebraic expressions and use exponents Algebraic expressions can be used to represent a situation in which the actual numerical value used may change. A power is written using a base and an exponent. The exponent is the number of times you multiply the base by itself Essential Question: How do you evaluate algebraic expressions and powers? To evaluate an algebraic expression, substitute the given value for the variable and then perform the operation. To evaluate a power, multiply the base by itself the number of times indicated by the exponent.