MATHS PROJECT

EXPONENTS AND POWERS

MADE BY :A.SAMUEL PRABHU DASS

LAW I:PRODUCT LAW

Examples: 1)x4 · x5 = x4+5 = x9 2)55 · 58 = 55+8 = 513

3)a7 · a · a12 = a7+1+12 = a20

4) (3x6)(2x4) = (3·2)x6+4= 6x10

am · an = am+n (when multiplying like bases, add the powers)

LAW II: QUOTIENT LAWAM = AM - N (WHEN DIVIDING WITH LIKE BASES, SUBTRACT THE POWER)AN (NOTE: IT IS ALWAYS THE NUMERATOR'S POWER MINUS THE DENOMINATOR'S POWER)

Example:1) x6 ÷ x4 =  x2          

LAW III:POWER LAW(ambm)n = amnbmn

(when taking a monomial to a power, multiply the powers including the coefficient) EXAMPLES1) (a4b3)2 = a8b6

2) (3m2n5)4 = 34m8n20 = 81m8n20

3) (-2xy7z2)5 = (-2)5x5y35z10 = -32x5y35z10

POWERS WITH DIFFERENT BASE

ZERO POWER RULE

a0  =   1  (any term to the zero power is one)

Examples: 1)  (m5 n7)0  =  1  2) (4m8n2)(-2mn4)0 = (4m8n2)(1) =4m8n2

 

NEGATIVE POWER RULE

a-n  =   1   and  1    =an (take the reciprocal of the variable to the negative power) NOTE: Apply the negative power rule to only negative POWERS