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 = With a real number a , a m (n a ) m n a m (m and n are positive integers in lowest terms) n Example: Use radical notation to rewrite each expression and simplify if possible. 93/2= 1 4 3 -2563/4= (-32)2/5= (2x + 1)2/7= 7x1/5= 2 = 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 = Summary of Exponent Rules Product rule for exponents: Power rule for exponents: Power rule for products & quotients: Quotient rule for exponents: Negative exponent: 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 Examples: Use the properties of exponents to simplify. x1/3 x1/4 = 9 9 2 5 12 = 5 2 (112/9)3 = (3x 3 ) 3 = x2 y-3/10 * y6/10 = 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 = Examples: Use rational exponents to write as a single radical y 3 y = 3 x 4 x = 5 3 2 =