Negative and Fractional Indices Worksheet
Practice problems for understanding and applying negative and fractional indices in mathematics for Grade 11 students.
Includes
Standards
Topics
Negative and Fractional Indices
Name:
Date:
Score:
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.
Related Worksheets
Classification of Real Numbers
A Grade 11 math worksheet covering the classification of real numbers, including natural, whole, integers, rational, and irrational numbers.
Irrational Numbers Worksheet
This worksheet focuses on understanding, identifying, and performing operations with irrational numbers for Grade 11 students.
Binary Number System Worksheet
Understanding and converting between binary and decimal number systems for Grade 11 students.
Opposite Integers Worksheet
Explore the concept of opposite integers, their properties, and their representation on a number line.