Evaluate Powers Expressions: (4/9)^(3/2) and (-27)^(-1/3)

[Raza]

Evalulate, leaving the answer as a fraction:


a) \left(\frac{4}{9}\right)^\frac{3}{2}


b) (-27)^-^\frac{1}{3}

Please Help.
Thanks

 

[Imo]

Some useful hints:

a^\frac{b}{c} = (a^b)^\frac{1}{c} = (a^\frac{1}{c})^b

a^-^b = \frac{1}{a}^b

a^\frac{1}{b} = \sqrt<b>{a} </b>

hope that helps

 

[Jameson]

And to add on to Imo's hints, remember that an exponent is written in the form of \frac{\mbox{power}}{\mbox{root}}

For instance, 9^{\frac{3}{2}} = (\sqrt{9})^3

 

[Raza]

Thank you, I finally got it. I lost my math notes and my exam is coming pretty soon so I needed to review.

 

[whozum]

a^-^b = \frac{1}{a^b} = \left(\frac{1}{a}\right)^b