MathsFreePrintable

Powers and Fractional Equations

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Powers and Fractional Equations

Show your working and give exact answers where possible. When solving equations with fractional powers, check that your answers satisfy the original equation.

Decode the index laws

Use the laws of indices to simplify each expression. Assume variables are non-zero where needed.

1.A code lock displays 3² × 3⁵. Simplify this to a single power of 3, then calculate its value.

2.A sensor records (a⁴)³. Simplify the expression as a single power of a.

3.Choose the expression equivalent to 27^(2/3).

(∛27)²
27 ÷ 2
√(27³)
2∛27

4.A cube-root calculation gives 64^(1/3). Work out its value. Then explain briefly what the exponent 1/3 means.

Crack the fractional-power equations

Use roots and powers to solve. Pay attention to whether an equation can have more than one real solution.

5.Solve x^(1/2) = 7 for the real value of x.

6.Solve x^(2/3) = 9, giving all real solutions. Check both answers in the original equation.

7.A machine follows the rule ½x^(1/2) = 4. Solve for x.

8.A value is transformed by adding 1 and then raising to the power 3/2: (x + 1)^(3/2) = 8. Solve for x, remembering that x + 1 must be non-negative.

Final code challenge

Combine index rules and fractional powers to unlock the final result.

9.Simplify completely: (8x⁶)^(2/3) ÷ (2x²)^(1/3), for x > 0.

2 printable pages

Download now

About This Worksheet

Free in Kuraplan

Print-Ready

Formatted for standard paper. Clean layout, easy to read.

AI-Generated

Created with Kuraplan's AI, designed for real classroom use.

For Teachers & Parents

Use in classrooms, for homework, tutoring, or homeschool.

Need a custom version of this worksheet?

Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.

Generate Custom Worksheets — Free

No credit card Curriculum-aligned Under 60 seconds

More Maths Worksheets

Powers and Fractional Equations

Powers and Fractional Equations

Decode the index laws

Crack the fractional-power equations

Final code challenge

2 printable pages

About This Worksheet

Free in Kuraplan

Print-Ready

AI-Generated

For Teachers & Parents

Need a custom version of this worksheet?

More Maths Worksheets

Understanding Fractions Worksheet

Exploring Fractions Deeply

Fractions and Plotting Practice

Fractions and Decimals Quiz

Basic Fractions Activity Sheet

Understanding Quarters Worksheet

Basic Fractions Practice Worksheet

Fractions and Probability Operations

Explore more free resources