Exponents Power exponent 5 3 base Example: 125 53 means that 53 is the exponential form of the number 125. 53 means 3 factors of 5 or 5 x 5 x 5 The Laws of Exponents: #1: Exponential form: The exponent of a power indicates how many times the base multiplies itself. n x x x x xxxx n times n factors of x 3 Example: 5 5 5 5 #2: Multiplying Powers: If you are multiplying Powers with the same base, KEEP the BASE & ADD the EXPONENTS! m n x x x So, I get it! When you multiply Powers, you add the
exponents! m n 2 6 23 2 63 29 512 #3: Dividing Powers: When dividing Powers with the same base, KEEP the BASE & SUBTRACT the EXPONENTS! m x m n m n x x x n x So, I get it! When you divide Powers, you subtract the exponents! 6 2 6 2 4 2 2 2 2 16
Try these: 12 2 2 1. 3 3 2. 52 54 3. 5 2 a a 2 7 4. 2 s 4 s 2 7. 8. 12 8 9. 3 5. ( 3) ( 3) 6. 2 4 7 3 s t s t s
4 s 9 3 5 3 s t 4 4 st 5 8 10. 36a b 4 5 4a b SOLUTIONS 2 2 22 a a a 5 2 4 1. 3 3 3 3 81 24 6 2 4 5 2. 5 5 5 3. 5
2 2 a 7 4. 2 s 4 s 2 4 s 2 3 5. ( 3) ( 3) ( 3) 6. 2 4 7 3 7 2 7 2 3 8s 9 5 ( 3) 243 s t s t s 27t 43 s 9t 7 SOLUTIONS 12 7. 8. 9. 10.
s 12 4 8 s s 4 s 9 3 9 5 4 3 3 81 5 3 12 8 s t 12 4 8 4 8 4 s t s t 4 4 st 5 8 36a b 5 4 8 5 3 36 4 a b
9 ab 4 5 4a b #4: Power of a Power: If you are raising a Power to an exponent, you multiply the exponents! n m x So, when I take a Power to a power, I multiply the exponents x 3 2 mn (5 ) 5 32 5 5 #5: Product Law of Exponents: If the product of the bases is powered by the same exponent, then the result is a multiplication of individual factors of the product, each powered by the given exponent. xy So, when I take a Power of a
Product, I apply the exponent to all factors of the product. n n x y 2 n 2 ( ab) a b 2 #6: Quotient Law of Exponents: If the quotient of the bases is powered by the same exponent, then the result is both numerator and denominator , each powered by the given exponent. x y So, when I take a Power of a Quotient, I apply the exponent to all parts of the quotient. n n x n y 4
4 16 2 2 4 81 3 3 Try these: 5 2 5 1. 3 2. a 3 4 3. 2 a 2 3 5 3 2 4. 2 a b 2 s 7. t2 39
8. 5 3 2 2 8 5. ( 3a ) 2 4 3 6. s t 2 st 9. 4 rt 5 8 2 36a b 10. 4 5 4a b SOLUTIONS 2 5 1. 3 3 4
2. a 2 3 12 a 2 3 3. 2 a 10 3 2 a 5 3 2 4. 2 a b 23 8a 2 22 a 52b 32 2 4 a10b 6 16a10b 6 2 2 2 5. ( 3a ) 3 a
2 4 3 6. s t 6 23 43 s t 22 9a 6 12 s t 4 SOLUTIONS 5 s 7. t 5 s 5 t 2 9 3 8. 5 34 3
2 8 3 2 4 2 2 8 st st s t 9. 4 2 r rt r 8 5 8 36a b 10 4 5 4a b 2 9ab 3 2
2 2 32 9 a b 2 6 81a b #7: Negative Law of Exponents: If the base is powered by the negative exponent, then the base becomes reciprocal with the positive exponent. So, when I have a Negative Exponent, I switch the base to its reciprocal with a Positive Exponent. Ha Ha! If the base with the negative exponent is in the denominator, it moves to the numerator to lose its negative sign! x m 1 m x 1 1 5 3 5 125 and 1 2 3
9 2 3 3 #8: Zero Law of Exponents: Any base powered by zero exponent equals one. 0 x 1 So zero factors of a base equals 1. That makes sense! Every power has a coefficient of 1. 50 1 and a 0 1 and (5a ) 0 1 Try these: 1. 2. 3. 2 2a b 2 0
y 2 y 4 5 1 a 2 7 4. s 4s 5. 3 x y 2 6. 3 4 2 4 0 s t 1 2 7. x 2 39 8. 5 3 2 2 2 s t 9. 4 4 s t 2 5 36a 10. 4 5
4a b SOLUTIONS 0 1. 2 a b 1 3. a 2 5 1 1 5 a 2 7 4. s 4 s 4s 5. 3x y 2 3 4 2 4 0 6. s t
5 3 x y 1 4 8 12 8 x 81y12 SOLUTIONS 2 1 2 7. x 9 2 3 8. 5 3 2 2 1 x 4 4 x 4 2
3 2 1 3 8 3 8 s t 2 2 2 4 4 s t 9. 4 4 s t s t 2 10 5 b 2 2 10 36a 9 a b 2 10. 4 5 81 a 4a b
an illustration - this type of drawing can be used for a product specification OR as a presentation drawing - which could be used to sell/promote the calendar. This type of drawing demonstrates it's use/function, illustrating a potential type of...
mth 101/l8 Basic Counting Principles Suppose an event ?1 can occur in ?1ways, a second event ?2 can occur in ?2 ways, and, following ?2; a third event ?3 can occur in ?3 ways, and soon.
Cardiac Conduction System (1) Conduction System of Heart Conduction System = Heart Beat & Pumping Cardiac Contractions = Unconscious Autonomic Nervous System decrease or increase heart rate depending on circumstance (2) Depolarization of the Heart Generate Action Potential & Depolarization:...
Work of slaves primarily agricultural. In 1860, ¾ of white people in South did not own slaves. Slaves concentrated in hands of relatively few. Bulk of staple crops produced on large plantations. Owners dominated political and economic thinking. Field Hands....
What level of complexity is necessary for life? THE CELL THEORY « Omnis cellula e cellula » Is the cell really that autonomous? Cellular components Plasmodesmata Acellular organisms Slide 18 Slide 19 Homeostasis Tissue culture THE ORGANISMAL THEORY SUMMARY SUMMARY...
Kristen Miller (FDA CDER) Laura Podolsky (Science37) Vaishali Popat (FDA CDER) ... Review state laws regarding direct-to-patient shipment. ... Reference Penny's earlier statement that recommendations include several specific examples of FDA meeting types and relevant offices. 6) Safety ...
Angle Pair Relationships Geometry BCHS I can: Identify vertical angles and linear pairs. Use vertical angles and linear pairs to find measures of angles. Which angles are adjacent? Linear Pair (of angles) 2 adjacent angles whose non-common sides are opposite...
Download Presentation
Ready to download the document? Go ahead and hit continue!