1 4 Powers and Exponents Objective Evaluate expressions

1 -4 Powers and Exponents Objective Evaluate expressions containing exponents. Holt Algebra 1

1 -4 Powers and 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. Holt Algebra 1 3 2 The exponent, 2 tells how many times the base, 3, is used as a factor.

1 -4 Powers and Exponents When a number is raised to the second power, we usually say it is “squared. ” The area of a square is s s = s 2, is the side length. S 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 = s 3 is the side length. S S S Holt Algebra 1

1 -4 Powers and Exponents Example 1 A: Writing Powers for Geometric Models Write the power represented by the geometric model. 5 53 Holt Algebra 1 The figure is 5 units long, 5 units wide, and 5 units tall. 5 5 5 The factor 5 is used 3 times.

1 -4 Powers and Exponents Example 1 B: Writing Powers for Geometric Models Write the power represented by the geometric model. 6 6 62 Holt Algebra 1 The figure is 6 units long and 6 units wide. 6 x 6 The factor 6 is used 2 times.

1 -4 Powers and Exponents Check It Out! Example 1 Write the power represented by each geometric model. The figure is 2 units long and 2 units wide. 2 2 a. 22 The factor 2 is used 2 times. b. x x x 3 Holt Algebra 1 x The figure is x units long, x units wide, and x units tall. x x x The factor x is used 3 times.

1 -4 Powers and Exponents 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. Holt Algebra 1

1 -4 Powers and Exponents Example 2: Evaluating Powers Evaluate each expression. A. (– 6)3 (– 6)(– 6) Use – 6 as a factor 3 times. – 216 B. – 102 – 1 • 10 – 100 Holt Algebra 1 Think of a negative sign in front of a power as multiplying by a – 1. Find the product of – 1 and two 10’s.

1 -4 Powers and Exponents Check It Out! Example 2 Evaluate each expression. a. (– 5)3 (– 5)(– 5) Use – 5 as a factor 3 times. – 125 b. – 62 – 1 6 6 – 36 Holt Algebra 1 Think of a negative sign in front of a power as multiplying by – 1. Find the product of – 1 and two 6’s.

1 -4 Powers and Exponents Example 2: Evaluating Powers Evaluate the expression. C. 2 2 9 9 2 2= 9 9 Holt Algebra 1 Use 2 as a factor 2 times. 9 4 81

1 -4 Powers and Exponents Check It Out! Example 2 Evaluate the expression. c. Use 3 as a factor 3 times. 4 27 64 Holt Algebra 1

1 -4 Powers and Exponents 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. Holt Algebra 1

1 -4 Powers and Exponents 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)4 Holt Algebra 1 The product of four – 3’s is 81.

1 -4 Powers and Exponents Check It Out! Example 3 Write each number as a power of a given base. a. 64; base 4 4 The product of three 4’s is 64. 43 b. – 27; base – 3 (– 3)(– 3)3 Holt Algebra 1 The product of three (– 3)’s is – 27.