Evaluate 78 × a10b 7c12 54 ×74 × 27 125×52 × a 7
- (a)
- (b)
- (c)76 × a 8b 4c12 8×49×53 103 × a 4 34 ×123 × 36 6×10 25 154 × 183
- (d)(e) × (f) 25 × 63 22 × 53 27 33 × 52 ×122 64 ×92 ×253 (g) 32 ×42 ×156 Look for a pattern in the table to extend what you know about exponents to find more about negative exponents. 10 2 101 10 0 10 –1 10 –2 10 –3 10 * 10 10 1 1 2000 100 10 1 1 1 1 = 0.1 = 0.01 = 0.001 10 100 1000 ÷10 ÷10 ÷10 ÷10 ÷10 15-04-2018 Any number that has an exponent of 0 is equal to 1. 1 So, 2 = 1, 3 = 1, 10 = 1, = 1. 0 0 0 2 For any number a ≠ 0, a0 = 1. You can show this by using the division of powers rule. If you start with 1000, and keep dividing by 10, you get this pattern: 1000 = 103 Now divide by 10 : 103 ÷ 101 = 10(3 – 1) = 102 100 = 102 Now divide by 10 : 102 ÷ 101 = 10(2 – 1) = 101 10 = 101 Now divide by 10 : 101 ÷ 101 = 10(1 – 1) = 100 1 = 100 When you divide 10 by 10, you have 101 ÷ 101 = 10(1–1) = 100. You also know that 10 divided by 10 is 1. So you can see that 100 = 1. This pattern works for any base. For instance, 61 ÷ 61 = 6(1–1) = 60, and 6 divided by 6 is 1. 6 0 = 1.
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(a)
(b)
(c) 76 × a 8b 4c12 8×49×53 103 × a 4 34 ×123 × 36 6×10 25 154 × 183
(d) (e) × (f) 25 × 63 22 × 53 27 33 × 52 ×122 64 ×92 ×253 (g) 32 ×42 ×156 Look for a pattern in the table to extend what you know about exponents to find more about negative exponents. 10 2 101 10 0 10 –1 10 –2 10 –3 10 * 10 10 1 1 2000 100 10 1 1 1 1 = 0.1 = 0.01 = 0.001 10 100 1000 ÷10 ÷10 ÷10 ÷10 ÷10 15-04-2018 Any number that has an exponent of 0 is equal to 1. 1 So, 2 = 1, 3 = 1, 10 = 1, = 1. 0 0 0 2 For any number a ≠ 0, a0 = 1. You can show this by using the division of powers rule. If you start with 1000, and keep dividing by 10, you get this pattern: 1000 = 103 Now divide by 10 : 103 ÷ 101 = 10(3 – 1) = 102 100 = 102 Now divide by 10 : 102 ÷ 101 = 10(2 – 1) = 101 10 = 101 Now divide by 10 : 101 ÷ 101 = 10(1 – 1) = 100 1 = 100 When you divide 10 by 10, you have 101 ÷ 101 = 10(1–1) = 100. You also know that 10 divided by 10 is 1. So you can see that 100 = 1. This pattern works for any base. For instance, 61 ÷ 61 = 6(1–1) = 60, and 6 divided by 6 is 1. 6 0 = 1.