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 simplifythe 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.

Question

klhsdvdsv · Answer

Please help,
 anyone,if possible.

klhsdvdsv · Answer

Please help....anyone out there?There's many of you "just looking around".I know there has to be someone out there that can help at any rate.

SmokeyBrown · Answer

Hi, and welcome to QuestionCove!

We can represent the expressions in the following form:
First, Megan's expression.
$$x ^{1/3} / x ^{1/12}$$
When we divide radicals of the same base, like in this example, we can simplify the expression by simply subtracting the power of the denominator from the power of the numerator. In other words, our result would be equal to:
$$x ^{1/3 - 1/12} $$
or
$$x ^{3/12} $$
or
$$x ^{1/4} $$

SmokeyBrown · Answer

Julie's expression, on the other hand, gives us the following:
$$\sqrt[32]{x}  * x ^{2}  * x ^{5}$$
Well, the square root part can actually be rewritten as 
$$ x ^{1/32}$$
to give us
$$x ^{1/32}  * x ^{2}  * x ^{5}$$
This, we can simplify by adding the exponents, since radicals of the same base are being multiplied together.
The result of this would be
$$x ^{1/32 + 2 + 5}$$
Which comes out to
$$x ^{7+1/32}$$

Comparing the two simplified expressions, it seems pretty clear that Megan and Julie did not start with equivalent expressions

klhsdvdsv · Answer

@smokeybrown Thank you for the explanation and for taking time out of your day to kindly help me out on my question,I really do appreciate it.
Have a good rest of your day.

SmokeyBrown · Answer

No problem. I hope you have a good day too :)