Reviewing the Exponent Laws

63 Integral Exponents Any number which can be expressed using a base and an exponent is called a power. 63 Exponents are used to show repeated multiplication. The exponent tells you how many times to use the base as a factor.

Exponent Laws or Properties Product Property: In multiplication, when the bases are the same, add the exponents. Quotient Property: In division, when the bases are the same, subtract the exponents. Power Property: When the base is a power, and it is raised to another exponent, multiply the exponents.

Exponent Laws Power of a Product: Remember that everything within the brackets is considered part of the base. Apply the Power Property to all the terms within the brackets. Power of a Quotient: Follow the same rules as a power of a product.

Exponent Laws Zero Property: Any base with a zero exponent has a value of 1. Negative Exponents: Change the numbers with negative exponents to numbers with positive exponents by reciprocating the base.

Exponent Laws Things to watch for when evaluating powers:

Simplifying Algebraic Expressions Using the Power Laws (2x3y2)(3x2y4) = (3x2y2)3 x (-2x3y)2 = (-3xy2)(-2x2y)2 =

Evaluating Expressions Using the Power Laws 5-2 -8a0 -32 -( 3 )0 50 + 5-1 -6-2 (2-2 + 32 - 5-1)0 32 + 23 + 40

Evaluating Algebraic Expressions Evaluate for a = 2 and b = 3: Example: 2ab2 =

Rewriting Powers to a Specified Base Express the first number as a power of the second: 81, 3 81 = 25, 5 25 Express as a power of 2: 162 x 323 x 8-4 Express as a power of 3. 272 x 814 x 93 2432 =

Applying the Exponent Laws

Simplifying and Evaluating Expressions with Powers 1. 2a2 x 6a3 2. (3a2b3c0)3 4. (1 - 1)3 x (-1)2 3. -6a5 x 2a2 6. -24 x -33 5. (-1)9 x (-1)4 7. 5-3 8. -6a0 10. -5-2 9. a-3 x a4 12. (-22)3 11. (-5)-2 14. -3a2b3 ÷ a-2b4 13. 8a10 ÷ 4a3

Evaluating Expressions with Powers 3-2 + 4 -1 52 + 5-1

Evaluating Expressions with Negative Exponents Or

Writing Answers With Positive Exponents When the exponent is negative in the numerator, move it to the denominator to make it positive. When the exponent is negative in the denominator, move it to the numerator to make it positive.

Simplifying Expressions to a Given Power Express as a power of 2:

Assignments Page 64 – 68: Page 73 - 76: 1ac, 2, 3begi, 1-4, 5bd, 6bde, 4-8, 10, 11, 12abcghi, 13ab,14bc, 15-18, 19bdf, 20, 21 Page 73 - 76: 1-4, 5bd, 6bde, 7, 8acfg, 9, 10, 12, 13ad Page 80 - 83: 1, 2, 3, 4abcfg, 5, 7cdgh, 8, 9, 10bdf, 11ab, 12ac, 13acf, 14a, 15, 16

Scientific Notation Scientific Notation is a method of expressing very large or very small numbers in a compact form. To be in scientific notation a number is expressed as a product of a number between 1 and 2 and a power of 10. 1.236 x 106 1.342 x 10-5 145 320 000 000 0.000 000 000 000 046 15.26 x 107 0.024 x 10-8

Calculating with Scientific Notation

Assignment Page 89- 92: 1, 2, 5, 8acegi, 9ace, 10bd, 11ac, 12bd, 13, 15