7.5 Properties of Exponents and Scientific Notation

Exponents and Exponential Expressions Exponents are used to write products of repeated factors. Ex. 3 • 3 • 3 • 3 = 34 In the above example, the 4 is the exponent and 3 is the base. The quantity 34 is called an exponential expression.

Evaluating Exponential Expressions Evaluate each exponential expression. 72 -42 (-2)4

 Evaluate each exponential expressions. 51 53 -84 (-2)5 -24

The Product Rule Product Rule for Exponents: am • an = am + n Apply the product rule for exponents in each case. 34 • 37 (5y2)(-3y4)

Apply the product rule for exponents in each case. 53 • 5 y3 • y8 • y2 (7p3q)(2p5q2)

The Power Rules Power Rules for Exponents

Applying the Power Rules Simplify each expression. (p8)3 (3y)4

 Simplify each expression.

Zero and Negative Exponents Zero Exponent a0 = 1 Negative Exponent Special Rules for Negative Exponents

Evaluating Exponential Expressions Evaluate each expression. 120 5z-3 -60 (-m)-4 (8k)0 2-3 3-1 + 4-1

Evaluate each expression. (5z)-3 (-6)0 -m-2 50 + 120 6-1 3-2 5-1 – 2-1

The Quotient Rule Quotient Rule for Exponents

Applying the Quotient Rule Simplify each quotient.

Simplify each quotient.

Writing Expressions with No Negative Exponents Simplify each expression so that no negative exponents appear in the final result. 32 • 3-5 (x-4)6

Simplify each expression so that no negative exponents appear in the final result. x-3 • x-4 • x2 (4-2)-5 (23x-2)-2

Scientific Notation Many of the numbers that occur in science are very large or very small. Writing these numbers is simplified by using scientific notation. Scientific Notation A number is written in scientific notation when it is expressed in the form a x 10n, where 1 ≤ |a|< 10 and n is an integer.

Converting to Scientific Notation Convert each number from standard notation to scientific notation. 8,200,000 .000072

Convert each number from standard notation to scientific notation. 46,500 .0051

Converting from Scientific Notation Convert each number from scientific notation to standard notation. 6.93 x 105 4.7 x 10-6

Convert each number from scientific notation to standard notation. 2.317 x 105 1.63 x 10-4

Using Scientific Notation in Computation Evaluate by using scientific notation.

Evaluate the following by using scientific notation.