Fractional and Negative Indices

Fractional and Negative Indices

Read each question carefully and answer to the best of your ability. Show all your working out where necessary.

1. Simplify the following expressions, leaving your answers with positive indices:

a) $x^{\frac{1}{2}} \times x^{\frac{3}{2}}$

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

c) $\frac{a^5}{a^{\frac{1}{2}}}$

2. Evaluate the following expressions without using a calculator:

a) $16^{\frac{1}{4}}$ =  

b) $27^{-\frac{2}{3}}$ =  

c) $(\frac{4}{9})^{-\frac{1}{2}}$ =  

3. Which of the following is equivalent to $\frac{1}{\sqrt[3]{x^2}}$?

4. State whether each statement is True or False:

a) $8^{\frac{2}{3}} = 4$

b) $5^{-2} = \frac{1}{25}$

5. Solve for $x$ in the following equations:

a) $x^{\frac{1}{3}} = 2$

b) $4^x = \frac{1}{16}$