7-3: Rational Exponents

For any nonnegative number, b ½ = Write each expression in radical form, or write each radical in exponential form ▫81 ½ = = 9 ▫ = 38 ½ ▫12m ½ = 12 ▫ = (32w) ½

1) Write 16 ½ in radical form

7-3: Rational Exponents n th root: If a n = b, then ▫Because 2 4 = 16, then Example ▫Simplify  Calculator: use the button (shift, ^)  Root comes first, then, then number under root  ▫Simplify 

2) Simplify

7-3: Rational Exponents For any positive real number b, and any integer n > 1, Examples ▫Simplify  ▫Simplify  = 2401 ^ (1/4) = 7

3) Simplify

7-3: Rational Exponents For any positive real number b, and any integers m and n > 1, Example ▫Simplify  or 32^(2/5) = 4

4) Simplify , ,743,392,201

5) Simplify

7-3: Rational Exponents Assignment ▫Page 410 ▫1 – 11 & 17 – 43 (odds)

7-3: Rational Exponents Day 2

7-3: Rational Exponents Power Property of Equality ▫b x = b y if and only if x = y  Example: If 5 x = 5 3, then x = 3  If the bases are equal, then their exponents are equal Example 1 ▫Solve 9 x = 729  Want both bases to be 9  9 1 = 9, 9 2 = 81, 9 3 = 729 ▫9 x = 9 3 ▫x = 3

7-3: Rational Exponents Example 2 ▫1▫16 2x – 1 = 8 AA base of 8 won’t work (8 1 = 8, 8 2 = 64) BBoth 16 and 8 can be written with bases of 2 22 4 = 16 & 2 3 = 8 ▫(▫(2 4 ) 2x – 1 = 2 3 ▫2▫2 8x – 4 = 2 3 Multiply exponents 88x – 4 = 3 88x = 7Add 4 to each side xx = 7 / 8 Divide each side by 8

Solve 5 x =

Solve 3 x+3 =

Solve 2 3x+10 =

Assignment Page 411 ▫45 – 53, odds