Laws of Exponents Worksheets
Free printable laws of exponents worksheets with answer keys. Use the laws of exponents: when you multiply powers of the same base, add the exponents (a^m ×…
Using this page
Use the laws of exponents: when you multiply powers of the same base, add the exponents (a^m × a^n = a^(m+n)), and when you divide, subtract them (a^m ÷ a^n = a^(m−n)). Answers are written as a single power. Exponents are taught in Class 7 and Class 8 in India (NCERT) and the Year 8 to Year 9 indices strand in Australia.
Tips
- Show the working, even when the answer seems obvious; it makes mistakes easy to spot.
- Check each answer: put it back into an equation, or estimate before working out.
- Start with the easier setting and move up once most answers are right.
- Mix one older sheet into each week so earlier skills stay fresh.
Worked example
3⁴ × 3² = 3^(4+2) = 3⁶. 5⁷ ÷ 5³ = 5^(7−3) = 5⁴.
Common mistakes
Multiplying the exponents instead of adding them.
Changing the base. The base stays the same when you multiply or divide.
How to use this generator
Choose the options above the sheet: the number of questions and the settings for this kind of worksheet. Every change makes a new sheet straight away, and New worksheet gives a different set of questions with the same settings.
Each sheet has a worksheet number printed at the top. Type the same number later, or keep the page link, to print exactly the same questions and answer key again. Leave Answer key page ticked to print the answers on a second page, then press Print. Every printed page carries the makekite logo and web address.
Common questions
What if the bases are different?
The laws only work when the bases are the same. These sheets always use the same base.
Can I make the sheet harder?
Yes. Use the options above the sheet: more digits, a harder level, brackets or negative numbers where they are offered.
Can I print the same worksheet again?
Yes. Note the worksheet number printed at the top, or keep the link in your browser's address bar, which ends with that number. Entering it later gives the same questions and answers.
Is it free?
Yes. There is no sign-up, and nothing you choose is sent anywhere: the sheets are made in your browser.