Simplify the following radical, fraction, exponent problems

Question

Bring to simplest form:

 

2

____     =

1-3√2

 

 

Simplify:

 

 

³√(x⁶y³)^{2 =}

 

 

(x⁶y3)^2/3 =

Answer 1

2 / (1 - 3√2)

 

√2 = 1.4142

 

1 - 3(1.4142) = -3.2426

 

2 / -3.2426 = - 0.6168

OR--Did you want an expression as a function of √2?

 

Simplify ³√(x⁶y³)²

 

first, recognize that the cube root of X can be written as x^(1/3).  Thus, we can write the expression as (x⁶y³)^(2/3)

 

next, note that raising something to a power means that the exponents are multiplied.  Therefore we can re-write like this:

 

x^(6)(2/3) y^(3)(2/3)

 

which is x⁴ y²