More with Exponents and Scientific Notation MATH 017 Intermediate Algebra S. Rook

2 Overview Section 5.2 in the textbook –Power rule for exponents –Solve more complicated expressions by combining exponent rules –Multiply and divide numbers written in scientific notation

Power Rule

4 Consider (x 2 ) 4 x2 x2 x2 x2x2 x2 x2 x2 Use the product rule: x 8 Power rule: (x a ) b = x ab Power of a product: (xy) b = x b y b Power of a quotient: (x / y) b = x b / y b Only applied when b is a power outside parentheses and not attached to a base Common mistake is to confuse the product and power rules

5 Power Rule (Example) Ex 1: Simplify – leave NO negative exponents: (6a -3 b 4 ) 2

6 Power Rule (Example) Ex 2: Simplify – leave NO negative exponents: (r 2 s -2 ) -3

Combining Exponent Rules

8 We have discussed three main rules: –Product: x a x b = x a+b –Quotient: x a / x b = x a-b –Power: (x a ) b = x ab When solving more complicated expressions: –Simplify inside of the parentheses using the product and quotient rules if possible –Use the power rule if applicable Apply the positive power Apply the -1 last if the exponent is negative –If necessary, write the final answer with positive exponents

9 Combining Exponent Rules (Example) Ex 3: Simplify – leave NO negative exponents:

10 Combining Exponent Rules (Example) Ex 4: Simplify – leave NO negative exponents:

11 Combining Exponent Rules (Example) Ex 5: Simplify – leave NO negative exponents:

12 Combining Exponent Rules (Example) Ex 6: Simplify – leave NO negative exponents:

Multiplication and Division with Scientific Notation

14 Multiplication and Division with Scientific Notation Multiply or divide the numbers as normal Use the product or quotient rules to simplify the power of tens Write the final answer in scientific notation

15 Multiplication and Division with Scientific Notation (Example) Ex 7: Perform the indicated operation and leave in scientific notation: (0.16 x )(0.03 x )

16 Multiplication and Division with Scientific Notation (Example) Ex 8: Perform the indicated operation and leave in scientific notation:

17 Multiplication and Division with Scientific Notation (Example) Ex 9: Perform the indicated operation and leave in scientific notation:

18 Summary After studying these slides, you should know how to do the following: –Apply the power rule to simplify expressions –Use the product, quotient, and power rules to simplify more complex expressions –Multiply and divide numbers written in scientific notation