Main Idea and New Vocabulary Example 1: Write Expressions Using Powers Example 6: Evaluate Powers Example 7: Evaluate Powers Example 8: Real-World Example Key Concept: Order of Operations Example 9: Evaluate Algebraic Expressions Example 10: Evaluate Algebraic Expressions Lesson Menu

Use powers and exponents to write large and small numbers. base exponent Main Idea/Vocabulary

Write Expressions Using Powers Write 7 • 7 • 7 • 7 using exponents. The base 7 is a factor 4 times. So, the exponent is 4. 7 • 7 • 7 • 7 = 74 Answer: 74 Example 1

Write 11 • 11 • 11 • 11 • 11 • 11 using exponents. A. 6 • 11 B. 611 C. 116 D. 117 Example 1 CYP

Write Expressions Using Powers Write (–9)(–9)(–9) using exponents. The base –9 is a factor 3 times. So, the exponent is 3. (–9)( –9)(–9)= (–9)3 Answer: (–9)3 Example 2

Write (–4)(–4)(–4)(–4)(–4) using exponents. A. (–4)4 B. (–4)5 C. (–4)(5) D. 5–4 Example 2 CYP

Write Expressions Using Powers Write a • a • a • a • a using exponents. The base a is a factor 5 times. So, the exponent is 5. a • a • a • a • a = a5 Answer: a5 Example 3

Write y • y • y • y • y • y • y using exponents. A. y7 B. y6 C. 7y D. 7y Example 3 CYP

Write Expressions Using Powers Write 4 • 4 • 6 • 6 • 6 • 6 • 6 using exponents. 4 • 4 • 6 • 6 • 6 • 6 • 6 = (4 • 4) • (6 • 6 • 6 • 6 • 6) Associative Property = 42 • 65 Definition of exponents Answer: 42 • 65 Example 4

Write (–2) • (–2) • (–2) • 7 • 7 using exponents. A. (–2) • 7 B. (–2)3 • 73 C. (–2)3 • 72 D. (–2)(3) • 72 Example 4 CYP

Write Expressions Using Powers Write x • y • x • y • x • x using exponents. x • y • x • y • x • x = x • x • x • x • y • y Commutative Property = (x • x • x • x) • (y • y) Associative Property = x4 • y2 Definition of exponents Answer: x4 • y2 Example 5

Write j • j • k • k • j using exponents. A. j • k B. 3j • 2k C. j3 • k2 D. j2 • k3 Example 5 CYP

(–5)2 = (–5) • (–5) Write the power as a product. = 25 Multiply. Evaluate Powers Evaluate (–5)2. (–5)2 = (–5) • (–5) Write the power as a product. = 25 Multiply. Answer: 25 Example 6

Evaluate (–4)5. A. –1,024 B. –20 C. 625 D. 1,024 Example 6 CYP

Write the power as a product. Evaluate Powers Evaluate . Write the power as a product. Multiply. Answer: Example 7

Evaluate . A. B. C. D. Example 7 CYP

2 • 42 • 52 = 2 • 4 • 4 • 5 • 5 Write the power as a product. RACQUETBALL A racquetball court has an area of 2 • 42 • 52 square feet. What is the area of the racquetball court? 2 • 42 • 52 = 2 • 4 • 4 • 5 • 5 Write the power as a product. = 2 • (4 • 4) • (5 • 5) Associative Property = 2 • 16 • 25 or 800 Multiply. Answer: The racquetball court has an area of about 800 square feet. Example 8

GARDENS A community vegetable garden has an area of 3 • 43 • 62 square feet. What is the area of the garden? A. 72 square feet B. 1,152 square feet C. 1,296 square feet D. 6,912 square feet Example 8 CYP

Key Concept 9

Evaluate Algebraic Expressions Evaluate x3 + y5 if x = 4 and y = 2. x3 + y5 = 43 + 25 Replace x with 3 and y with 2. = (4 • 4 • 4) + (2 • 2 • 2 • 2 • 2) Write the powers as products. = 64 + 32 or 96 Add. Answer: 96 Example 9

Evaluate a4 – b2 if a = 3 and b = 5. C. 4 D. 2 Example 9 CYP

Evaluate Algebraic Expressions Evaluate (x + y)2 if x = 4 and y = 2. (x + y)2 = (4 + 2)2 Replace x with 4 and y with 2. = 62 Perform operations in the parentheses first. = 6 • 6 or 36 Write the powers as products. Then simplify. Answer: 36 Example 10

Evaluate (r + s)4 if r = –3 and s = 7. B. 81 C. 256 D. 10,000 Example 10 CYP