# Powers Expressions

1. May 12, 2005

### Raza

Evalulate, leaving the answer as a fraction:

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

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

Thanks

2. May 12, 2005

### Imo

Some useful hints:

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

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

$$a^\frac{1}{b} = \sqrt{a}$$

hope that helps

3. May 12, 2005

### 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, $$9^{\frac{3}{2}} = (\sqrt{9})^3$$

4. May 12, 2005

### Raza

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

5. May 12, 2005

### whozum

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