Tiêu đề 01_VI_E-TEC_VOL-2_ALG_W.S-1-10_PG_1-50.pdf ✅

VI-Mathematics (Vol- 2) e-Techno Text Book 2 Example: 5 2 2 2 2 2 2      Here 2 2 2 2 2     is called the product form (or) expanded form and 25 is called the exponential form. Note: * The first power of a number is the number itself. i.e., a1 = a. * The second power is called square. Example: Square of ‘3’ is 32 * The third power is called cube. Example: Cube of x is x3 * 1 raised to any integral power gives ‘1’ Example: 1100 = 1 * (– 1)odd natural number = –1 Example: (– 1)375 = –1 * (– 1)even natural number = 1 Example: (– 1)2010 = 1 Note: 1) m m 1 we have a a   where m is a positive integer and a is a non zero integer then we say m a  is the multiplicative inverse of m a . 2) m n If a a then m n   If bases are equal are in equation form, then equation the powers. 3) If n n x y y x               Laws of Exponents (or) Indices: 1. The product of the two powers of the same base is a power of the same base with the index equal to the sum of the indices. i.e., If a 0  be any rational number and m, n be positive integers, then m n m n a a a    2 × 2 = (2 × 3 4 2 × 2)(2 × 2 × 2 × 2) = 2 = 2 + 2 a × a = (a × a)(a × a × a) = a = a In General x × x = x . 7 3 4 2 3 2 + 3 5 m n m + n 2. Where m, n are positive integers, x 0. 
e-Techno Text Book VI-Mathematics (Vol- 2) 3 3. Power of Product:   n n n ab a b   where a 0, b 0   , and n is a positive integer Example:   4 5 6                5 6 5 6 5 6 5 6 5 5 5 5 6 6 6 6           = 54 × 64 . 4. Quotient of powers of the same base. m n m n n m a if m n a 1 a if n m a           Example: 4 2 4 2 2 7 7 7 7 7 7 7 7 7 7         . 5. Power of a quotient i.e., m m m a a b b        where a 0, b 0   , and m is a positive integer. Example: 3 3 3 5 5 5 5 5 4 4 4 4 4           . 6. Powers with exponent zero: If we apply the above laws of indices of evaluate m n a a where m = n, and a 0  then m m n 0 n a a a 1 a     Example: 40 = 1, 0 x 1 y        etc ... 7. 8.