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Using a Power EXAMPLE 3 Cliff Height A stone falls over the edge of a cliff next to a waterfall. The stone hits the water 5 seconds later. How tall is the cliff? To find the height of the cliff use the expression 16 t 2, the distance in feet that an object falls in t seconds after it begins to fall. Substitute 5 for t. Evaluate the power. =16 (25) = 400 Multiply. The height of the cliff is 400 feet.ANSWER 16 t 2 = 16 (5) 2

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Using the Order of Operations EXAMPLE 4 a. (6 - 4) 3 3 2 2 + – 8 3 4 = + – = 7 Evaluate inside grouping symbols. Evaluate powers. Add and subtract from left to right. Evaluate the expression. = –2323 + 32

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Using the Order of Operations EXAMPLE 4 Evaluate inside grouping symbols. 16= 3.3 64 = 13.2 Evaluate powers. Multiply and divide from left to right. b. 3.3 (7 1) 2 4 2 += 3.3 8 2 42

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GUIDED PRACTICE for Examples 3 and 4 (5 2) 3 7 4 3 – – +8. Evaluate the expression. Evaluate inside grouping symbols. (3) 3 – 7 + 4 3 = = 27 – 7 + 64 Evaluate powers. = 20 + 64 Subtract. = 84 Add.

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GUIDED PRACTICE for Examples 3 and 4 Evaluate the expression. 12.3 + (4 + 2) 2 2 4 – 9. – 12.3 + (6) 2 2 4 = = 12.3 + 36 – 16 = 12.3 +20 Evaluate inside grouping symbols. Evaluate powers. Add. = 32.3

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GUIDED PRACTICE for Examples 3 and 4 Evaluate the expression. 10. 7 3 + 24 (7 6) 4 – = 7 3 + 24 (1) 4 = 7 3 +24 = 343 + 24 = 367 Evaluate inside grouping symbols. Evaluate powers. Add.

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GUIDED PRACTICE for Examples 3 and 4 11. What If? Suppose the falling stone in Example 3 took 8 seconds to hit the water. Evaluate the expression to find the height of the cliff. 16 t 2 Substitute 8 for t. Evaluate the power. =16 (64) = 1024 Multiply. The height of the cliff is 1024 feet.ANSWER = 16 (8) 2

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Divide. Evaluate power. 27 3 2 2 – 3 = 27 9 2 – 3 EXAMPLE 1 27 9 2 – 3 = 3 2 – 3 3 2 – 3 = 6 – 3 Multiply. Evaluate expressions Multiply and divide from.

Divide. Evaluate power. 27 3 2 2 – 3 = 27 9 2 – 3 EXAMPLE 1 27 9 2 – 3 = 3 2 – 3 3 2 – 3 = 6 – 3 Multiply. Evaluate expressions Multiply and divide from.

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