Click on the correct answer.
You will see the left side of an equation. Then you will see and hear two possible answers for the right side of that equation.
Click on the correct answer.
There are 10 questions in this test.
to start the lesson
Secondary math lessons to learn
'Divide Indices' for 8th grade
8th grade / Number / Powers & Roots / Indices / Divide Indices
Divide indices with the same base by subtracting powers
What are indices?
Indices are terms that have been raised to a power such as 5⁶ or y⁴. This means the term has been multiplied by itself that number of times.
6⁴ = 6 x 6 x 6 x 6 and y⁵ = y x y x y x y x y
So the term indice simply means a number or term raised to a power.
How to divide indices with the same base
Indices with the same base can be divided by subtracting powers. So a³ and a⁶ have the same base "a", but x³ and y⁶ do not have the same base and cannot be simplified by subtracting powers.
To understand why dividing indices with the same base involves subtracting powers, consider x⁷ ÷ x⁴. If we expand both indices we get:
x x x x x x x x x x x x x
x x x x x x x
Since we know that x divided by x is 1, we can cancel terms top and bottom to simplify the expression leaving x x x x x.
x⁷ ÷ x⁴ = x³
So we can see that dividing x⁷ by x⁴ gives us x³. In general, you can divide indices with the same base by subtracting the powers.
If one or more of the terms is raised to a negative power, you should follow simple arithmetic rules to subtract the powers.
p⁻⁵ ÷ p³ = p⁻⁸
p⁻⁵ ÷ p⁻³ = p⁻²
If there are coefficients in front of the bases, divide the coefficients first and then subtract the powers.
15p⁵ ÷ 3p³ = 5p⁵
With these interactive math lessons you will be learning "Divide Indices" from
8th grade / Number / Powers & Roots in 3 easy steps. The math in our lessons consists of 6 questions that ask you to divide indices with the same base by subtracting powers e.g. 6b⁵ ÷ 2b² = 3b³.
There are 3 easy math lesson activities in this "Divide Indices" tutorial. These activities progress step by step to help you the learner gradually master this math topic. The activities are based on "3 stage questioning", a method of learning that quickly and easily builds your confidence as you work through the short series of lessons that strengthen your knowledge of the math that you want to learn.
When you have completed the tutorial for a topic, you should try some of our games before finally doing the test for your chosen topic. See the Help box below for detailed instructions on how to use the lesson activities to help you learn your math more easily.
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'Divide Indices' for 8th grade
Introduction to the math topic
You start the tutorial with a lesson that introduces the math you will be learning. You will see a set of questions one at a time, and for each question you will see the written answer and also hear the answer to that question.
Repeat the question/answer by clicking on the brown speaker sign. Repeat the question/answer and expand the question graphic by clicking on the question box. Move between questions using the arrow buttons below the question. If there is additional information available for your chosen topic, the "i" button on the left upright bar will be brown on white. Click on the button to load the additional lesson information into the main interface.
Either / Or math lesson
This lesson moves on from the "Introduction" lesson and offers you two possible answers to each question. So, you will see a question then a voice will ask "Is this ... or is it ..." and you will have to choose which of the answers is the one that matches the question.
You choose an answer by clicking or tapping on one of the two answer boxes below the question. You can play the audio for each answer again by clicking on the speaker icon beside the written answer (if robot speech is available and enabled). The program will let you know each time whether you answered correctly. A star will light up red for a wrong answer or white/black for a correct answer.
This lesson asks you the questions in a random order compared to the introduction. At the end of the lesson, you can choose whether to repeat the lesson or move on to the next one.
What is it? math lesson
The final lesson of the tutorial shows you multiple possible answers for each question - you must choose the correct one. You are asked a question and below it are a list of two, three, or four possible written/numeric answers from this topic. Pressing the speaker icon will play the math audio for that answer.
For each picture, click on the answer that matches the question. The program will tell you whether you are right or not. As with the Either / Or activity a system of stars indicate your right and wrong answers. The What is it? lesson will show you all the questions you learned in the Introduction but in a random order.
When you complete the "What is it?" lesson, you can choose whether to go on to play some games with this topic, or whether you want to repeat some or all of the lesson activities in this tutorial. You should expect to get 80% of the answers correct in most of the activities before trying some of the Math games with this topic.
