Objective Evaluate expressions containing exponents.

A power is an expression written with an exponent and a base or the value of such an expression. 3² is an example of a power. The base is the number that is used as a factor. 3 2 The exponent, 2 tells how many times the base, 3, is used as a factor.

When a number is raised to the second power, we usually say it is “squared.” The area of a square is s  s = s2, is the side length. S When a number is raised to the third power, we usually say it is “cubed.” The of volume of a cube is s  s  s = s3 is the side length. S

Example 1A: Writing Powers for Geometric Models Write the power represented by the geometric model. The figure is 5 units long, 5 units wide, and 5 units tall. 5  5  5 5 53 The factor 5 is used 3 times.

Example 1B: Writing Powers for Geometric Models Write the power represented by the geometric model. 6 The figure is 6 units long and 6 units wide. 6 x 6 6 62 The factor 6 is used 2 times.

Check It Out! Example 1 Write the power represented by each geometric model. a. The figure is 2 units long and 2 units wide. 2  2 22 The factor 2 is used 2 times. x b. The figure is x units long, x units wide, and x units tall. x  x  x x The factor x is used 3 times. x3

Caution! In the expression –52, 5 is the base because the negative sign is not in parentheses. In the expression (–2), –2 is the base because of the parentheses. If the negative is NOT inside parentheses, the answer is NEGEATIVE not matter what.

Example 2: Evaluating Powers Evaluate each expression. A. (–6)3 (–6)(–6)(–6) Use –6 as a factor 3 times. –216 B. –102 Think of a negative sign in front of a power as multiplying by a –1. –1 • 10 • 10 Find the product of –1 and two 10’s. –100

Check It Out! Example 2 Evaluate each expression. a. (–5)3 (–5)(–5)(–5) Use –5 as a factor 3 times. –125 b. –62 Think of a negative sign in front of a power as multiplying by –1. –1  6  6 Find the product of –1 and two 6’s. –36

Example 2: Evaluating Powers Evaluate the expression. C. 2 9  Use as a factor 2 times. 2 9 = 4 81 2 9 

Check It Out! Example 2 Evaluate the expression. c. Use as a factor 3 times. 3 4 27 64

If there is an EVEN number of negatives multiplying, then the answer is POSITIVE. If there is an ODD number of negatives multiplying, then the answer is NEGATIVE.

Example 3: Writing Powers Write each number as a power of the given base. A. 64; base 8 8  8 The product of two 8’s is 64. 82 B. 81; base –3 (–3)(–3)(–3)(–3) The product of four –3’s is 81. (–3)4

Check It Out! Example 3 Write each number as a power of a given base. a. 64; base 4 4  4  4 The product of three 4’s is 64. 43 b. –27; base –3 (–3)(–3)(–3) The product of three (–3)’s is –27. (–3)3