1. When you simplify 8 23, what is the ones digit? COURSE 2 LESSON 3-7 You know that 8 23 is a large number to calculate. You need to find out what number is in the ones place. It is not easy to simplify 8 23 with paper and pencil. You could simplify easier expressions, like 8 2, 8 3, and 8 4, to see what number is in the ones place. 3-7 Solve a Simpler Problem and Look for a Pattern

2. (continued) COURSE 2 LESSON 3-7 Power Value 8 1 8 8 2 64 8 3 512 8 4 4,096 8 5 32,768 8 6 262,144 8 7 2,097,152 8 8 16,777,216 8 9 134,217,728 8 10 1,073,741,824 Step 1: Solve a Simpler Problem Find the values of the first 10 powers of 8. Refer to the table at the right. Notice that the ones digits in the value column repeat in the pattern 8, 4, 2, 6. 3-7 Solve a Simpler Problem and Look for a Pattern

3. (continued) COURSE 2 LESSON 3-7 Step 2: Look for a Pattern Organize the information to see whether there is a connection between the ones digits and the exponents. Refer to the table at the right. Ones PlaceExponent of 8 81, 5, 9 42, 6, 10 23, 7 64, 8 If the exponent is divisible by 4, then the ones digit is 6. Since 20 is divisible by 4, you can start there: Exponent:20212223 Ones digit:6842 The number in the ones place of 8 23 is 2. 3-7 Solve a Simpler Problem and Look for a Pattern

4. (continued) COURSE 2 LESSON 3-7 Look for a pattern in another row of the exponent table that might also work. When the exponent of 8 is 2, 6, or 10, the ones digit is 4. The numbers 2, 6, and 10 are divisible by 2, but not by 4. Since 22 is divisible by 2 but not by 4, the ones digit of 8 22 is 4. Exponent:2223 Ones digit:42 3-7 Solve a Simpler Problem and Look for a Pattern

5. 1.What is the eighth number in the pattern: 5, 25, 125, 625, 3,125, 15,625,...? 2.A jump-rope manufacturer has invited 128 teams to participate in a rope-jumping contest. Teams are paired, and any team that loses one match is eliminated from the contest. How many matches are needed to determine the winner? COURSE 2 LESSON 3-7 390,625 127 3-7 Solve a Simpler Problem and Look for a Pattern