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Rational Exponents

Week 1 The Math standard covered this week is: " Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents." Common Core Math Standard  N.RN.1 

Key Points
1. When changing form from radical to rational exponents, the “root” is the denominator of the fraction.
changing the rational exponent  p^2/3 to a radical
2. When simplifying a cube root, find 3 common factors, then bring them out the radical. Multiply the remaining factors and leave them under the radical.  
3.Use the calculator to evaluate exponents or radicands. Enter a rational (fractional) exponent using parenthesis.
converting 3xcube root of 32
entered as 32 ^(2/5)
32^2/5
Rational Exponents
How to evaluate rational exponents and radicals
Video Guide
0:18 Problem 1. Evaluate negative nine times the seventh root of one
0:52 Problem 2 Evaluate the cube root of 64 squared. This problem gives step by step directions on how to enter this problem on a TI30sx calculator.
2:00 Problem 3 Evaluate 125 to the 1/3 squared
2:43 Problem 4 Evaluate 2 over 2 to the negative 2. 
This problem involves working with a negative exponent.

Video Tutorials covering radicals,rational exponents,cubed roots

How to simplify square and cube roots
Video covers how to simplify square and cube roots. One of the problems simplifies a square root of a fraction
Video Guide
0:09 Simply 3 x the cube root of 32
1:20 Simplify 4 x the cube root of 27
1:59 Simplify the square root of 18x over a^6


Rational expressions to radicals
Video reviews how to move rational expressions to radical form and a radical to a rational expression
0:48 Change p^2/3 to a radical
1:08 Change 2^2/5 to a radical
1:28 Change 17^1/6 to a radical
1:50 Change 20^1/2 to a radical
Next, the video switches to the opposite and shows how to move from a radical to a rational expression
2:20 Express cube root of 22 to the third power to a rational
2:26 Express square root 113 as a rational
3:02 Express square root of 5 raised to the third as a rational
3:14 Express fifth root of z^4 as a rational



right arrow pointing from radical expression to rational expression