moomoomath logo header
lime green horizontal line
Welcome to MooMooMath
Quick Math Homework Help
Geometry Coach
geometry coach lesson plans

Rational Exponents

Week 2 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 point #1:

When simplifying expressions containing exponents,
first, apply the exponents to all terms in the parenthesis, including the coefficients.  

Second, raise the coefficient to the exponent, but multiply the exponent. 
Key point #2:

When simplifying a radical expression to a cube root or 4th root, find groups:
Ex. Cube root: Find groups of “3” by factoring into prime factors

Video gives step by step directions for solving "Operations with Radicals"
Video Guide
0:19 This problem involves adding and subtracting radicals 
6 x cube root of 3 -cube root of 3 +4x square root of 3
Remember that you can only combine like terms.
1:03 This problem involves multiplying like terms
6 x square root 7 x -1/2 x square root 7
Remember multiply outside times outside coefficients and inside times inside coefficients
1:49 This problem involves dividing radicals square root 3/square root 15
Remember you can't have a radical on the bottom of the fraction so you have to rationalize 
3:05 Involves subtracting radicals

Video Tutorials "Radicals and Exponents"

How to simplify a radical expression
Video Guide
0:08 Simplify the radical 6 times the square root of 49e^10f^7
Step one is to find perfect squares so that you can bring factors out.
1:37 This problem involves a fourth root,so you will looking for groups of four. Fourth root of 32x^8y

​This Video works several problems in which you simplify fractions with exponents and then tackles simplifying radicals.

Video Guide
0:22 Simplify -24a^2b^-3/ 16a^7
1:13 Simplify This problem involves an exponent raised to an exponent (5xy^-4)^-2
2:16 Simplify fractional exponents 2y^3/5/y^1/4

Simplifying expressions containing exponents (2x^3y^4)^4-2^4x^3y^4-16x^12y^16
2*3*3*3 x*x*x* x*x*x* x y*y*y*y

So from each group of 3 we bring out of the radical a 3 x*x and y but there is a 2, x and y left under the radical.

radical cube root of 54^7y^4
multiplying radicals 3^2yxcube root 2xy