Algebra 2 Ration Exponents

Question

Megan and Julie are stuck simplifying radical expressions. Megan has to simplify the quantity of x to the one third power, over x to the one twelfth power. Julie has to simplify the thirty second root of the quantity of x times x to the second times x to the fifth. Using full sentences, describe how to fully simplify Megan and Julie's expressions. Describe if Megan and Julie started with equivalent expressions or if they started with expressions that are not equal.

Answer 1

Well, when you divide exponents with the same base, you sbtract the exponents.

 

For example, a³/a² = (a(a)(a))/(a(a)). 

 

a/a = 1, so it cancels out twice and leaves us with a/1 = a, which also equals a¹.

 

x^1/3/x^1/12 = x^{1/3 - 1/12} = x^{4/12 - 1/12} = x^3/12 = x^1/4

 

When you multiply, you add the exponents.

 

a³(a²) = a(a)(a)(a)(a) = a⁵

 

x^1/32(x²)(x⁷) = x^{9 1/32} = x^289/32, or the 32nd root of x raised to the 9th power.