Starter (On your own paper) Solve for x. 4 𝑥−3 = 𝑥−3 𝑥−3 + 1 𝑥−3 January 9, 2015

Questions?

Examples 1 𝑥 3𝑥 + 2 4 = 3 6 − 1 2𝑥 1+ 1 2𝑛 = 2 𝑛

Examples 2 1 3 − 1 3𝑎 = 2 𝑎 1 𝑎+6 −1= 2 𝑎+6

Simplifying Radicals 𝑛 𝑥 Examples: 2 36 3 27 4 16 If the index is odd, the answer can be positive or negative If the index is even, the answer can only be positive

Multiplying & Dividing Radicals Multiplication 2 ∙ 3 = 2∙3 3 4 ∙ 3 5 = 3 4∙5 Division 2 3 = 2 3 3 4 3 5 = 3 4 5

Adding & Subtracting Radicals 4 2 +3 2 =7 2 4 3 4 +3 3 5 =4 3 4 +3 3 5 Example: 5 3 +2 75 Are the radicals the same? No. Can we simplify either radical? Yes. Now are the radicals the same?

Rational Exponents 𝑛 𝑥 𝑎 = 𝑥 𝑎 𝑛 1 𝑥 2 = 𝑥 −2 1 𝑛 𝑥 𝑎 = 𝑥 − 𝑎 𝑛 Example: 64 1 2 = 2 64 =8 1 4 = 1 2 2 = 2 −2 1 ( 𝑣 ) 3 = 𝑣 −3 = 𝑣 −3 2