# Exponents Power exponent 5 3 base Example: 125 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