The Secret to Using the Power of a Power Rule for Exponents
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How to use the Power of a Power Rule for Exponents
There is a simply formula when using the Power Rule for simplifying exponents. In order to use the Power Rule for exponents, you keep the base of the power the same and you multiply the exponents. Always remember to be careful of the sign of the exponents.
Common Core Standard: 8.EE.A.1
The Quick Power of a Power Rule Definition
So what is the power rule for exponents anyway? There is a basic equation when using the Power Rule for solving exponential problems. When using the Power to a Power Rule for exponents, you keep the base of the power the same and you multiply the exponents. Keep in mind the signs of the exponents since they can be positive or negative.
3 Steps for Solving the Power Rule Examples Problem
- When using the Power of a Power Rule for Exponents you must multiply the exponents together.
- You multiply whatever exponents is on the outside of the parenthesis to everything that is on the inside of the parenthesis.
- When multiplying, make sure you include any negatives if there are any.
Power of a Power Practice Problems Quiz
Watch the Power of a Power Rule Video Explanation
Watch our free video on how to use Power of Power Rule of Exponents. This video shows how to solve problems that are on our free Power to a Power worksheet that you can get by submitting your email above.
Watch the free Power of a Power video on YouTube here: Power of a Power
This video is about the power rule exponents. You can get the power rule exponents worksheet we use in this video for free by clicking on the link in the description below.
The first problem we’re going to work on on our power of a power rule of exponents worksheet is number two. This problem gives us 8 to the 8th raised to the 4th power. In order to simplify this problem you have to take the exponent that is on the outside of the parenthesis and distribute it to every exponent that is on the inside of the parenthesis. Now in the case of this example this is like saying we have 4 8 to the 8th powers. If we were to rewrite this we would rewrite it 8 to the eighth times itself 4 times. We have our 8 to the 8th right now and we wrote it out four times because it is being raised to the exponent of 4. You should remember from the product rule for exponents that whenever you multiply exponential terms you keep the base the same and you add the exponents. If we look at this problem we will keep the base of 8 and then we’re going to add all of the exponents together. 8 plus 8 plus 8 plus 8 is 32, so our answer would be 8 to the 32nd power.
Now there is a shortcut for solving the power rule of exponents that you can do by skipping this middle step here. If you look at our original problem we have 8 to the 8th raised to the 4th power and if you look at our answer 8 to the 32nd power you might notice that if we had multiplied 8 times 4 we could get 32. So instead of having to write it out and add the exponents together. The shortcut for the power power rule for exponents is to do just that, it is to multiply.
In the case of this problem 8 to the 8th with raised to the 4th power you can do 8 to the 8 times 4 which would be 8 to the 32nd power. That’s the same answer we got in our first step. Now that we know the shortcut for the power to power rule we can go ahead and do a couple other practice problems.
In the case of this problem we have X to the 6 raised to the third power. I told you anytime you have a parenthesis in between two exponents that means you’re going to multiply the exponents. This is like saying X to the sixth times three. Which would be X to the 18th power and that’s going to be your answer.
This is the last problem we’re going to go over. This problem gives us negative exponents. We have 4 to the negative 2nd raised to the negative 2nd power. We already learned that anytime that there is a parenthesis in between two exponents that means to multiply so we’re going to keep the rule the same. Even though we have negative exponents we’re still going to multiply the two exponents together. Now the only trick when you have negative exponents is that you must include the negative when you multiply the exponents together. We will do negative 2 times negative 2 and when we do negative 2 times negative 2 you will get a positive 4. The solution is 4 to the positive fourth power.
Power of a Power Rule
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