Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Section 7.2 (Rational Exponents) Example: Find (27)1/3 = (33)1/3 = With a real number a , a 1 n n a (n is a positive integer) Examples: Use radical notation to write the following and simplify if possible. 251/2= 641/3= x1/5= -251/2= (-27y6)1/3= 7x1/5= Example: Find 82/3 = (82)1/3 = m (n a ) m n a m (m and n are positive integers in lowest terms) With a real number a , In other words, given a number a raised to the m/n power, m (the numerator) is the power a is raised to, and n (the denominator) is the index of the root being taken You can raise a to a power first or take the root first (typically I will take the root first in order to keep the numbers small) a n Example: Use radical notation to rewrite each expression and simplify if possible. 93/2= (-32) -2563/4= 2/5 1 4 = (2x + 1)2/7= 3 2 = 7x1/5= With a real number a , a m n 1 a m (am/n is a nonzero real number) n Example: Write each expression with a positive exponent, and then simplify. 27-2/3= -256-3/4 = Book problems: 1, 3, 5, 11, 13, 15, 17, 19, 21, 27, 29, 33, 35, 39, 43, 45, 47, 49, 51 Summary of Exponent Rules am * an = am + n (am)n = am * n (ab)n = an bn (a/c)n = an / cn , c 0 am / an = am – n , a 0 a-n = 1 / an , a 0 Product rule for exponents: Power rule for exponents: Power rule for products & quotients: Quotient rule for exponents: Negative exponent: Examples: Use the properties of exponents to simplify. x 1/3 x 1/4 9 = 9 y-3/10 * y6/10 = 2 5 12 = 5 (112/9)3 = 2 (3x 3 ) 3 = x2 Examples: Multiply x3/4(x1/4 – x3) = (x1/4 + 1)(x1/4 – 7) = Example: Factor x-1/3 from the expression 7x-1/3 – 5x5/3 Some radical expressions are easier to simplify when we first write them with rational exponents Examples: Use rational exponents to simplify 10 y5 = 4 9= 9 a 6 n3 = Book problems: 1, 3, 5, 11, 13, 15, 17, 19, 21, 27, 29, 33, 35, 39, 43, 45, 47, 49, 51