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Slide 1: Rational Exponents Rational Exponents Made Easy
Slide 2: 1/2 5 Example of a Rational Exponent
Slide 3: Properties of Rational Exponents Property Example 31/2 ∙ 33/2 = 31/2+3/2 = 32 = 9 am∙an = am+n (am)n = amn (ab)n = ambn a-m = 1/am am/an = am-n (a/b)m = am/bm (43/2)2 = 4(3/2∙ 2) = 43 = 64 (9∙4)1/2 = 91/2∙41/2 = 3∙2 = 6 25-1/2 = 1/251/2 = 1/5 65/2/61/2 = 6(5/2 - 1/2) = 62 = 36 (8/27)1/3 = 81/3/271/3 = 2/3
Slide 4: Methods to Solve Rational Exponents Method One: Graphing Calculator This can be used only where bases are a number If the base is a variable only use it to calculate the fraction Method Two: Mathematical Process This can be used with variable or numerical bases
Slide 5: If x and y are positive real numbers, which expression is equivalent to (16x5y8)1/2? Method One: Calculator Enter 161/2 into the calculator and hit enter. Write the answer. Enter 5 times 1/2 into the calculator. Write the answer as the exponent of x. Enter 8 times 1/2 into the calculator. Write the answer as the exponent of y.
Slide 6: If x and y are positive real numbers, which expression is equivalent to (16x5y8)1/2? Method Two: Mathematical Process Find the root of the number. √16 = 4 Multiply the exponents of the variables. x(5∙ 1/2) y(8∙ 1/2) x5/2y4 Write the results. 4x5/2y4