Question

Please Help

Tyler1997
4.One of your friends sends you an email asking you to explain how all of the following expressions have the same answer.
3 sqwrt x^3
x^1/3*x^1/3*x^1/3
1/x^-1
11sqwrt x^5*x^4*x^2
Compose an email back assisting your friend and highlight the names of the properties of exponents when you use them.

Answer 1

by 3sqwrtA you mean
\[\sqrt[3]{A}\]
???
Cause that is called cubical root.
well if so then
cbrt(x^3) is a cubical root of the third power of x so it is equal to x.
Samewise the second one, since x^(1/3)=cbrt(3)
x(-1)=1/x
so if you divide 1/(1/x) Then it is equal x
x^a*x^b=x^(a+b)
thus
x^5*x^4*x^2=(x^5*x^4)*x^2=x^(5+4)*x^2=x^9*x^2=x^(9+2)
Now the root of eleventh degree from x^11 is also equal to x.
All those are equal to x so they are all equal to each other.