5 2 Apply Properties of Rational Exponents Do

5. 2 Apply Properties of Rational Exponents Do properties of exponents work for roots? What form must they be in? How do you know when a radical is in simplest form? Before you can add or subtract radicals what must be true?

Properties of Rational Exponents

This is a good example I why I have been complaining about the book slides. This is how it copies… Use the properties of rational exponents to simplify the expression. a. 71/4 71/2 = 7(1/4 + 1/2)= 73/4 b. (61/2 41/3)2 = (61/2)2 (41/3)2 = 6(1/2 2) 4(1/3 2) = 61 42/3 = 6 42/3 c. (45 35)– 1/5 = [(4 3)5]– 1/5 = (125)– 1/5 = 12[5 (– 1/5)] = 12 – 1 = 1 12 d. e. 51 = 5(1 – 1/3)= 52/3 = 51/3 421/3 2 42 1/3 2 = = (71/3)2 = 7(1/3 2) = 72/3 61/3 6 5 Now see what changes I made…

Use the properties of rational exponents to simplify the expression. = 7(1/4 + 1/2) = 73/4 b. (61/2 • 41/3)2 c. (45 • 35)– 1/5 = (61/2)2 • (41/3)2 = [(4 • 3)5]– 1/5 = 6(1/2 • 2) • 4(1/3 • 2) = (125)– 1/5 = 12[5 • (– 1/5)] = 61 • 42/3 = 6 • 42/3 = 12 – 1 = 1 12 d. 5 = 51/3 e. 51 = 5(1 – 1/3) = 52/3 51/3 421/3 2 42 61/3 6 = 1/3 2 = (71/3)2 = 7(1/3 • 2) = 72/3

Write the expression in simplest form You need to rationalize the denominator— no tents in the basement

Adding and subtracting like radicals and root. Ø When adding or subtracting like radicals the root and the number under the radical sign must be the same before you can add or subtract coefficients. Ø Radical expressions with the same index and radicand are like radicals. Ø You may need to simplify the radical before you can add or subtract.

Adding & Subtracting Roots and Radicals

Simplify the expression involving variables

Write the expression in simplest form

Add or subtract the expression involving variables.

• Do properties of exponents work for roots? Same rules apply. • What form must radical be in? Fractional exponent form • How do you know when a radical is in simplest form? When there are no more numbers to the root power as factors of the number under the radical. • Before you can add or subtract radicals what must be true? The number under the radicals must be the same.