Using a PowerEXAMPLE 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 16t 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

Using the Order of OperationsEXAMPLE 4

a. (6 - 4)3 3 22+ –

8 3 4 = + –

= 7

Evaluate inside grouping symbols.

Evaluate powers.

Add and subtract from left to right.

Evaluate the expression.

= – 23 + 3 22

Using the Order of OperationsEXAMPLE 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 42+ = 3.3 82 42

GUIDED PRACTICE for Examples 3 and 4

(5 2)3 7 43–– +8.

Evaluate the expression.

Evaluate inside grouping symbols.

(3)3 – 7 + 43=

= 27 – 7 + 64 Evaluate powers.

= 20 + 64 Subtract.

= 84 Add.

GUIDED PRACTICE for Examples 3 and 4

Evaluate the expression.

12.3 + (4 + 2)2 24–9. – 12.3 + (6)2 24=

= 12.3 + 36 – 16

= 12.3 +20

Evaluate inside grouping symbols.

Evaluate powers.

Add.

= 32.3

GUIDED PRACTICE for Examples 3 and 4

Evaluate the expression.

10. 73 + 24 (7 6)4– = 73 + 24 (1)4

= 73 +24

= 343 + 24

= 367

Evaluate inside grouping symbols.

Evaluate powers.

Add.

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