Fractional and Negative Indices
This worksheet focuses on understanding and applying fractional and negative indices to simplify expressions and solve equations.
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Fractional and Negative Indices
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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 $\frac{1}{\sqrt[3]{x^2}}$?
$x^{\frac{2}{3}}$
$x^{-\frac{2}{3}}$
$x^{\frac{3}{2}}$
$x^{-\frac{3}{2}}$
4. State whether each statement is True or False:
a) $8^{\frac{2}{3}} = 4$
True
False
b) $5^{-2} = \frac{1}{25}$
True
False
5. Solve for $x$ in the following equations:
a) $x^{\frac{1}{3}} = 2$
b) $4^x = \frac{1}{16}$