7 5 Fractional Exponents Algebra 2 0 What

7. 5 Fractional Exponents Algebra 2. 0 What? ! More Fractions? !

Main Idea & Vocabulary • The index is the small number to the left of the radical symbol that tells which root to take. • In a fractional exponent, the numerator is the power, and the denominator is the root. • It is easier to do the root first, then the power. • B 1/n = the root of the base • B m/n = the root and power of the base

Finding Squares • List the squares up to 30. 12 = 1 112 = 121 212 = 441 22 = 4 122 = 144 222 = 484 32 = 9 132 = 169 232 = 529 42 = 16 142 = 196 242 = 576 52 = 25 152 = 225 252 = 625 62 = 36 162 = 256 262 = 676 72 = 49 172 = 289 272 = 729 82 = 64 182 = 324 282 = 784 92 = 81 192 = 361 292 = 841 202 = 400 302 = 900 102 = 100

Common Powers • • • 23 = 8 24 = 16 25 = 32 26 = 64 27 = 128 28 = 256 29 = 512 210 = 1024 33 = 27 • • • 34 = 81 43 = 64 44 = 256 53 = 125 54 =625 63 = 216 73 = 343 83 = 512 93 = 729 Learn these well!!

Definition of b(1/n)

Ex 1 Simplifying b(1/n)

Practice 1

Definition of b(m/n)

Ex 2 Simplifying b(m/n) • Rewrite it as a root and a power.

Practice 2

Radical Expressions • To simplify radical expressions: 1) Take roots of regular numbers 2) Divide the exponents by the index 3) Leave remainders under the root Example:

Ex 4 Simplifying Expressions

Practice 4

Ex 3 - Application

Review • What is the index? • What does a fractional exponent of (1/n) represent? • What does a fractional exponent of (m/n) represent?