Exponents are math shortcuts that tell us how many times... Show more
Mathematics149 views·Updated May 19, 2026·1 pageUnderstanding the Laws of Exponents
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Laws Of Exponents
When numbers have exponents and you need to combine them, there are simple rules to follow. Think of these laws as math "shortcuts" that save you time and effort!
The first law tells us that when multiplying expressions with the same base, you add the exponents (3² · 3⁵ = 3²⁺⁵ = 3⁷). For division with the same base, subtract the exponents (3⁵ ÷ 3² = 3⁵⁻² = 3³).
When raising a power to another power, you multiply the exponents . With expressions like (3·4)², you can split it into 3² · 4². For fractions, the rule is similar: (³⁄₄)² = ³²/₄² = ⁹⁄₁₆.
Remember This! Negative exponents flip the fraction! When you see (³⁄₄)⁻² it equals (⁴⁄₃)², and ³⁻²/₄⁻⁵ equals ₄⁵/₃². This rule trips up many students, so practice it extra!
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Mathematics149 views·Updated May 19, 2026·1 pageUnderstanding the Laws of Exponents
Exponents are math shortcuts that tell us how many times to multiply a number by itself. The laws of exponents give us rules for working with these expressions, making complex calculations much simpler. These rules are super useful in algebra... Show more
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Laws Of Exponents
When numbers have exponents and you need to combine them, there are simple rules to follow. Think of these laws as math "shortcuts" that save you time and effort!
The first law tells us that when multiplying expressions with the same base, you add the exponents (3² · 3⁵ = 3²⁺⁵ = 3⁷). For division with the same base, subtract the exponents (3⁵ ÷ 3² = 3⁵⁻² = 3³).
When raising a power to another power, you multiply the exponents . With expressions like (3·4)², you can split it into 3² · 4². For fractions, the rule is similar: (³⁄₄)² = ³²/₄² = ⁹⁄₁₆.
Remember This! Negative exponents flip the fraction! When you see (³⁄₄)⁻² it equals (⁴⁄₃)², and ³⁻²/₄⁻⁵ equals ₄⁵/₃². This rule trips up many students, so practice it extra!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Similar Content
Most popular content in Mathematics
9Most popular content
9Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user