Exponential Equations with Same Base Worksheet + Answer Key

A no prep worksheet on solving exponential equations with a common base. The exercises require to use the properties of exponents in order to simplify the equations and solve them. There are 20 problems and detailed solutions are included.

This comprehensive, no-prep worksheet provides your students with targeted practice solving exponential equations by finding a common base. It builds fluency, confidence, and algebraic mastery in A-Level Mathematics, IB Diploma, and advanced GCSE classrooms.

What is Included

• 20 Strategic Practice Problems: A curated set of questions that systematically guide students from basic single-step equations to complex problems requiring fractional bases, negative exponents, and laws of indices.
• Full Step-by-Step Answer Key: A complete solution guide showing every algebraic transformation, base conversion, and linear step used for quick marking or student self-checking.
• Generous Workspace: Clean, structured grid layout providing students with ample room to rewrite their bases and solve for the variable clearly.

Perfect For

• Independent classwork or homework assignments
• Higher-tier GCSE or A-Level core algebra revision and retrieval tasks
• Hassle-free cover work and ready-to-use substitute teacher plans
• Targeted exam preparation for index laws and exponential functions

Aligned Educational Standards
UK National Curriculum & Specifications

• Key Stage 4 & A-Level Algebra: Understand and use the laws of indices; solve equations involving exponential terms by equating indices.
• GCSE Mathematics (AQA, Edexcel, OCR, Eduqas): Work with index laws; solve equations where the unknown is an index by converting to a common base.
• International Curricula (IB Diploma / IGCSE Extended): Apply properties of exponents and indices to transform and solve exponential functions without technology.