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

The Quotient Rule Quotient Rule for Exponents

Applying the Quotient Rule 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.

IB Exam Information (NOT in your book!) Express your answer in the form a x 10k, where 1 ≤ |a|< 10 and k Є . FYI: Є means “is an element of” represents “all integers”

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.