Laws of Exponents PDF

FLORAIDA M. NOLLEDO General Mathematics Teacher  Exponents exponent Power 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 Ex...

FLORAIDA M. NOLLEDO General Mathematics Teacher  Exponents exponent Power 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 xxxx 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 m n x x  x So, I get it! When you multiply Powers, you add the exponents! 26 23 263 29 512 #3: Dividing Powers: When dividing Powers with the same base, KEEP the BASE & SUBTRACT the EXPONENTS! m x m n m n n  x x  x x So, I get it! 6 When you divide 2 6 2 4 Powers, you 2  2 22 subtract the exponents! 16 Try these: 12 s 2 1. 3 3  2 7. 4  s 2. 52 54  3 9 8. 5  3. 5 a a  2 3 12 8 2 4. 2 s 4 s  7 s t 9. 4 4  st 2 3 5. ( 3) ( 3)  5 8 36a b 10. 4 5  6. 2 4 s t s t  7 3 4a b #4: Power of a Power: If you are raising a Power to an exponent, you multiply the exponents! x m n mn x So, when I take a Power to a power, I multiply the exponents #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. n  xy   x y n n So, when I take a Power of a Product, I apply the exponent to 2 2 2 all factors of the ( ab) a b product. #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. n n  x x    n  y y So, when I take a Power of a Quotient, I apply the exponent to 4 4 all parts of the  2 2 16    4  quotient.  3 3 81 Try these: 5  s 1. 3   2 5 7.    t2 2. a 3 4  39  8.  5   3. 2a   2 3 3  8 2 4. 2 a b   2 5 3 2  st  9.  4   2 2  rt  5. ( 3a )  5 8 2  36a b  10.    4 5    6. s t 2 4 3  4a b  #7: Negative Law of Exponents: If the base is powered by the negative exponent, then the base becomes reciprocal with the positive exponent. m 1 x  m So, when I have a Negative Exponent, I switch the base x to its reciprocal with a Positive Exponent. Ha Ha! 3 1 1 If the base with the negative 5  3  exponent is in the 5 125 denominator, it moves to the and numerator to lose its negative sign! 1 2 2 3 9 3 #8: Zero Law of Exponents: Any base powered by zero exponent equals one. 0 x 1 So zero factors of 50 1 a base equals 1. and That makes sense! Every power has a 0 1 a coefficient of 1. and (5a ) 0 1 Try these: 1 2 2  1. 2a b  2 0 7.     x  2 2. y 2 y  4   39  8.  5   3. a  5 1   3  2 2 2 2 4. s 4 s  7 s t  9.  4 4   s t  5. 3 x y   2 3 4  36a 5 2 10.  4 5   6. s t   2 4 0  4a b 