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## 1.2 Exponents and Powers

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**1.2 Exponents and Powers**Algebra 1 Concepts and Skills McDougal Littell Linda Stamper**An expression like 43 is called a power.**43 base exponent word form: four to the third power four cubed factor form (meaning): 4 • 4 • 4 evaluated form: 64**Example 1Express the power in words. Then write the meaning.**1. Write problem. 82 2. Write word form. eight squared 3. Write meaning. (factored form) 8 • 8**Example 2Express the power in words. Then write the meaning.**1. Write problem. 53 2. Write word form. five cubed 3. Write meaning. 5 • 5 • 5**Example 3Express the power in words. Then write the meaning.**1. Write problem. y4 y to the fourth power 2. Write word form. 3. Write meaning. y • y • y • y**A power applies only to what is directly in front of it.**Evaluate when x = 6. The problem. x2 Substitute. (6)2 Write factors. (6)(6) Simplify. 36 You could write in factored form and then substitute. x2 (6)(6) 36**When you evaluate exponential expressions, work within**grouping symbols first. ( ) , [ ] ,{ } Example 4Evaluate when m = 4 and n = 3. Remember: In algebra work downward. Highlight or circle your answer. Skip one line after the answer. 1. Write problem. (m + n)2 2. Substitute. ((4) + (3))2 3. Simplify within parentheses. (7)2 49 4. Evaluate power.**When you evaluate exponential expressions, work within**grouping symbols first. ( ) , [ ] ,{ } Example 5Evaluate when m = 4 and n = 3. (m2) + (n2) 1. Write problem. ((4)2)+ ((3)2) 2. Substitute. 3. Write factors. (4 • 4) + (3 • 3)Optional Step 16 + 9 4. Simplify within parentheses. 25 5. Simplify. When parentheses are nested work from the inside going out.**Example 6Evaluate when a = 5.**Remember a power applies only to what is directly in front of it! 1. Write problem. 2a2 2. Substitute. 2(5)2 3. Evaluate power. 2(25) 50 4. Simplify.**Example 7Evaluate when a = 5.**1. Write problem. (2a)2 2. Substitute. (2(5))2 3. Simplify within parentheses. (10)2 100 4. Evaluate power.**Example 8A box has the shape of a cube. Each edge s is 8**inches long. Find the volume in cubic inches. 1. Write formula. V = s3 2. Substitute. = (8)3 3. Write factors. Optional Step = 8 • 8 • 8 4. Simplify. = 512 5. Write a sentence. The volume of the box is 512 cubic inches. This cannot be written as 5123inches!**Homework**1-A2 Pages 12-14, # 1-57