Negative and Fractional Indices Worksheet
Practice problems for understanding and applying negative and fractional indices in mathematics for Grade 11 students.
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Negative and Fractional Indices
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Read each question carefully and provide your answer in the space provided. Show all your work for full credit.
Simplify the following expressions, writing your answers with positive indices only.
1. $x^{-5}$
2. $3a^{-2}$
3. $\frac{1}{y^{-3}}$
4. $(2b)^{-4}$
Simplify the following expressions, writing your answers in radical form where appropriate.
1. $16^{\frac{1}{2}}$
2. $27^{\frac{1}{3}}$
3. $64^{\frac{2}{3}}$
4. $(81x^4)^{\frac{1}{4}}$
Complete the following conversions.
1. $a^{\frac{m}{n}}$ in radical form is .
2. $\sqrt[3]{x^5}$ in index form is .
3. $p^{-q}$ in fractional form is .
4. $\frac{1}{m^n}$ in index form is .
1. Which of the following is equivalent to $4^{-2}$?
$-16$
$\frac{1}{16}$
$16$
$-8$
2. What is the value of $8^{\frac{2}{3}}$?
$2$
$4$
$8$
$16$
1. If $x^2 = 9$ and $y^3 = 8$, find the value of $x^{-1}y^{\frac{1}{3}}$.
2. Evaluate $\frac{5^{-2} \times 10^3}{2^{-3}}$ without using a calculator.