I really need help help with these two!

Question

Rewrite using radicals: (x^(3/4))(y^(1/4))
 
 
 

cuberoot(x^4)*sqrt(x^(1/2))
 

cuberoot(x^4)*y^4
 

cuberoot(x^4)*4throot(y)
 

4throot((x^3)y)
 

sqrt((x^(3/2))y)
 
 
Rewrite using rational exponents: sqrt((3xy)^4)
 
 
 

(3xy)^(1/2)
 

(xy)^(3/4)
 

3(x^2)(y^2)
 

9(x^2)(y^2)
 

81(x^2)(y^2)

Answer 1

Hi Caleb.

 

An exponent that is a fraction has a numerator (the power) and a denominator (the root).

 

A cube root is x^(1/3).  You could rewrite this as ³√x¹

 

If you have x^3/4, then you have the 4th root (the denom) of x³ (the numerator) 

 

You could write this as ⁴√(x³)

 

If you have y^1/4, then you have the 4th root (the denom) of y^{1 (the numerator)}

 

You could write this as  ⁴√(y¹)

 

Since both of these are a 4th root, you can combine them under one radical:

 

⁴√(x³ y¹)  or just  ⁴√(x³ y).

 

 

 

 

Sqrt is a power of 1/2.

 

So sqrt((3xy)⁴)  is the same as [(3xy)⁴]^1/2

 

Then you can multiply your exponents and get   

 

3^(1/2)x^(1/2)y^(4/2)

 

=3^(1/2) x^(1/2) y²