# Properties of Integers Properties of Integers Video Complete page 33 with a partner https://www.khanacademy.org/math/in-seve nth-grade-math/exponents-powers/laws-exp onents-examples/v/raising-a-number-to-the0th-and-1st-power Multiplying Numbers with Exponents

Page 34 PART A & C Product of Powers To multiply numbers with exponents that have the SAME BASE, ADD the exponents and keep the base same Examples: 23 27 2 2 2 2 2 2 2 2 2 2 =2

10 4 3 44 4 4 4 4 4 4 4 =47 (65)( 6) 6 6 6 6 6 = 66 X4 x 6 x x x x

=x 10 6 x x x x x x 23 25 2 2 2 2 2 2 2 2

28 (x3)(x4) x x x x7 x x x x What about those with coefficients? 2x3 4x5 = 8x8

6x4 5x7 = 30x11 -3y4 4y3 = -12y7 Power of Product To raise a product to a power, raise each

factor to the same power. (3 4)2 =32 42 = (5x)3 =52 x2 25 x2 =

144 Power of a Power This property is used to write an exponential expression as a single power of a base Example: (52)3 52 3 52 52 5 2 = 5 6

Example: (x2)4 x24 x2 x2 x2 x2 = x8 Review This property combines the first two multiplication properties to simplify exponential expressions (-6 5)

2 (-30)2= 900 (5xy) 3 5 5 5 x x x y y y 125x3y3 (4x2)3 x5

4 4 4 x2 x2 x2 x5 x x x x x x x x x 64x11 Division of Exponents Dividing Exponents To divide with exponents that have the same base, subtract the exponents of the same numerator from the exponent of the denominator and keep the base the same

Example: 3 33 3 3333 3 33 3 3 3 33 3 3333 3 33 3 3

33 = 1 27 Practice

= Practice = Practice

= Reciprocal Review What is the reciprocal? One of two numbers whose product is 1also called the multiplicative inverse

Examples: = 4= Negative Exponents

NEVER HAVE A NEGATIVE EXPONENT When dealing with negative exponents, (which is not mathematically correct) change it to a positive exponent. Negative Exponent Rules 1. Put the equation into a fraction

2. in order to get rid of a negative exponent, flip the base and exponent to complete the reciprocal 3. Once flipped, the negative exponent becomes positive Negative Exponents https://www.khanacademy.org/math/in-eight h-grade-math/exponents-powers-1/powers-n

egative-exponents/v/negative-exponents Examples x-3 y-5 Examples 3x-2

(3x)-2 = = The exponent in this example belongs only to the variable and not

to the coefficient (the base of three) Because of the parenthesis, the base of the example is everything inside the parenthesis. So, we move EVERYTHING inside the parenthesis Examples: =

= 4a6 Example A negative coefficient is very different from a negative exponent. ONLY NEGATIVE EXPONENTS MOVE...