Smartick Try it for free! Abrir el Menú Móvil Try it for free!
Accelerate your child’s learning
Smartick is a fun way to learn math!

Jun18

Properties of Powers II

In today’s post we’re going to continue talking about the properties of powers.

Before we go on, you might find it useful to review the concept of a power, its elements and how to solve them. You can take a look at these previous Smartick blog entries if you need a reminder:

Once you’re up to speed with all this information, we can move on.

Powers with a negative integer exponent

This property only applies to a power with a base that is not zero (0). When we find a base that meets this condition with a negative integer component, we can say that this power is equivalent to a fraction with a numerator of 1 and a denominator which is the given power, but with the sign of the exponent changed (from negative to positive). Powers

Let’s take a look at this property applied to a specific case. Here we can see that 3 to the power of minus 2 is the same as the fraction one over 3 squared:Powers

Powers of another power

As you can see here, a power of a power is the same as a power with the same base but with the two exponents multiplied by each other:

Powers

Let’s look at an example. If we raise 3 squared to the power of 3, we get the same result as if we raise 3 to the power of 6. In both cases, the result is 729.

Powers

Multiplying powers with the same exponent

Here we see that if we multiply two powers with the same exponent, we get the same product as if we multiply the bases first and then raise the result by the shared exponent.

Powers

Now let’s look at an example. We can see that multiplying 5 squared by 3 squared gives the same product as multiplying 5 by 3 and raising the result by 2.

Powers

Dividing powers with the same exponent

If we’re faced with a division between two powers with the same exponent, we’ll obtain the same quotient if we divide the bases first before elevating the result of the division by the shared exponent.

Powers

Take a look at this example. We get the same quotient if we divide 6 squared by 2 squared or if we divide 6 by 2 and then raise the result by 2. Take a look:

Powers

I hope this article has helped you learn the properties of powers!

Remember, if you want to practice primary math exercises, you can find them in our daily sessions. Log in to Smartick and try our online math learning method for free!

Learn More:

Fun is our brain’s favorite way of learning
Diane Ackerman
Smartick is a fun way to learn math
  • 15 fun minutes a day
  • Adapts to your child’s level
  • Millions of students since 2009
Share on FacebookTweet about this on TwitterShare on LinkedIn
Smartick

Add a new public comment to the blog:

The comments that you write here are moderated and can be seen by other users.
For private inquiries please write to [email protected]

Your personal details will not be shown publicly.

I have read and accepted the Privacy and Cookies Policy