Question

You have challenged four other students to come up with expressions equal to x2. Their submissions are below. :

Mike
x to the eight-fifths power times x to the four-fifths power, over x to the two-fifths power

Kelly
the seventh root of the quantity of x to the third times x to the fifth times x to the sixth

Scott
the sixth root of x, to the third power

Kim
the fifth root of x times x to the two-fifths power times x to the three-fifths power times x to the four-fifths power

Answer 1

Using complete sentences, explain the steps in simplifying the expression of each student and identify who is correct.

Answer 2

To simplify Kim's expression:
First write out the expression: 5sqrtx*x^2/5*x^3/5*x^4/5 Next get rid of the radical:
The square root of x = 1/2 but because there is a 5th root the x inside of the square root is x to the 1/5 power or x^1/5.
So now we have x^1/5*x^2/5*x^3/5*x^4/5 Add the powers:
x^1/5+2/5+3/5+4/5
which equals x^10/5
which simplifies to x^2

Answer 3

Let me solve the other ones hold on a few minutes

Answer 4

Are you in flvs algebra 2?

Answer 5

yeah!

Answer 6

module 2 exam?

Answer 7

yup

Answer 8

This will take me about 20 minutes to finish so hold up and work on you 4 other essays while you wait.

Answer 9

im actually all finished with the rest this is the only one im unsure of! But thank you so much!

Answer 10

No problem

Answer 11

To simplify Scott's expression:
First write out the expression: (6sqrtx)^3
The sqaure root of x is equal to x^1/2 but because there is a 6 instead of the given 2 6sqrtx is equal to x^1/6. Next you are going to multiply 3 into the x factor:
x^1/6*3= x^6/3 which fully simplified is x^2

Answer 12

To simplify Mike's expression:
First write out the expression: x^8/5*x^4/5 all over x^2/5
Multiply the top exponents together by adding the powers:
x^8/5*x^4/5=x^12/5
The expression now look like this: x^12/5 all over x^2/5
To divide you subtract the powers: 12/5-2/5 which equals x^10/5 which simplifies further to x^2

Answer 13

I'm almost done with Kelly's hang tight lol

Answer 14

To simplify Kelly's expression:
First write out the expression: 7sqrtx^2/3*x^5*x^6
You want to get the square root into exponential form before you can multiply the expressions together: 7sqrt^2/3=x^2/21. Once you have that you can multiply your powers:
x^5*x^6*x^2/21 Add the powers: 5/1+6/1+2/21= 13/21 which can not be further simplified so Kelly was incorrect. Her final answer was x^13/21

Answer 15

All finished there you go @emmii2239

Answer 16

May I get a medal? That wasn't just a short and sweet answer you know...