# Example 1 Evaluate a numerical expression       Name __________________________________ Date ___________________ LESSON 5.1 Study Guide GOAL Simplify expressions involving powers. Vocabulary A number is expressed in scientific notation if it is in the form c 10n where 1 c < 10 and n is an integer. EXAMPLE 1 Evaluate a numerical expression Negative exponent property = 36(– 4)3 Power of a power property = 729(–64) = – 46,656 Evaluate power. EXAMPLE 2 Use scientific notation in real life Hoover Dam The volume of concrete that was used to construct the Hoover Dam is about 3,325,000 cubic yards. One cubic yard of concrete weighs about 4050 pounds. About how many pounds of concrete were used to construct the Hoover Dam? Pounds of concrete Weight per cubic yard Number of cubic yards Solution = = 4050 3,325,000 Substitute Values =(4,05103)(3.325106) Write in scientific notation. =(4,053.325(103106) Use multiplication properties. =13.46625109 Product of powers property =1.346625101109 Write 13.46625 in scientific notation. =1.3466251010 Product of powers property The number of pounds of concrete is about 1.346625 1010, or about 13,466,250,000 pounds. LESSON 5.1 Study Guide continued EXAMPLE 3 Simplify an expression Simplify the expression. Tell which properties of exponents you used. Power of a power property = y7z0 Quotient of powers property = y7.1 Zero exponent property = y7 Identity property of multiplication EXAMPLE 4 Compare real-life volumes Softball The radius of a softball is about times the radius of a baseball. How many times as great as the baseball's volume is the Softball's volume? Solution Let r represent the radius of a baseball. Then r represents the radius of a softball. The volume of a sphere is πr3 (cancel common factors) = Power of a quotient and quotient of powers = Zero exponent property 2.370370 Use a calculator. The volume of a softball is about 2.37 times as great as the volume of a baseball.Download 17.33 Kb.Share with your friends: