convert to exponential form and simplify.

Question

Assume all variables represent positive numbers. (I'm not sure what that means)

 

 

a) (2√x)³/³√(x )

 

 

 

^{b) 6}√(y³ z)⋅√y/³√z

Answer 1

Variables being positive numbers just means that x, y, z are all greater than zero.

 a)  We can rewrite the expression as [2x^1/2 ]³ / x^1/3 = 2³ x^3/2 / x^1/3

      This now equals 8x^{3/2 - 1/3} = 8x^7/6

 

b)   we can rewrite the expression as (y³z)^1/6 * y^1/2 /z^1/3 =  y^1/2 z^1/6 * y^1/2 z^-1/3 = y^{1/2 + 1/2} * z^{1/3 - 1/3} = yz⁰ = y*1 = y