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6y³ x 7y²
= 42y⁵

Multiply indices
for 8th grade

Multiply indices with the same base by adding powers e.g. 5a³ x 6a² = 30a⁵

Multiply indices by adding powers

What are indices?

Indices are terms that have been raised to a power such as 5⁶ or x³ or 4y⁴. Raised to the power means the term has been multiplied by itself that number of times.

4³ = 4 x 4 x 4     and     a⁵ = a x a x a x a x a

So the term indice simply means a number or term raised to a power.


How to multiply indices with the same base

In order to be able to multiply indices by adding powers, the indices must have the same base. So a³ and a⁶ have the same base "a", but x³ and y⁶ do not have the same base and cannot be simplified using the methods on this page.

To see why we can add powers to multiply indices with the same base, consider the expression a³ x a⁴. If we expand both indices we get:

(a x a x a) x (a x a x a x a) = a x a x a x a x a x a x a = a⁷

So we can see that multiplying a³ x a⁴ gives us a multiplied by itself 7 times, which you will notice is the same as adding the powers of the two terms.

a³ x a⁴ = a⁷

y⁴ x y⁴ = y⁸

If one or more of the terms is raised to a negative power, you follow the standard rules of arithmetic to compute the powers through adding and taking away.

p⁵ x p³ x p⁻³ = p⁵

p⁻⁵ x p⁴ x p⁻³ = p⁻⁴

If there are coefficients associated with the indices, multiply the coefficients first then add the powers to simplify the expression.

6y⁴ x 7y⁴ = 42y⁸

7p⁵q³ x 4p⁻³q² = 28p²q⁵

Below is a table showing the first 6 question answer pairs for the topic "Multiply indices" as used in the lessons for this topic. Our games and tests for the topic use these 6 items plus 10 additional question answer pairs.

The topic "Multiply indices" is in the category Number for 8th grade (ages 13 to 14).

1 / 6
N² x N⁴ can be simplified to N
N² x N
N
2 / 6
3B³ x B³ can be simplified to 3B
3B³ x B³
3B
3 / 6
4E⁵ x 5E⁷ can be simplified to 20E¹²
4E⁵ x 5E
20E¹²
4 / 6
M⁻³ x -4M⁸ can be simplified to -4M
M⁻³ x -4M
-4M
5 / 6
BE² x BE² can be simplified to BE
BE² x BE²
BE
6 / 6
4M²N x -6M⁻⁴N can be simplified to -24M⁻²N²
4M²N x -6M⁻⁴N
-24M⁻²N²

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Each of our math topics for secondary are made up of between 6 and 20 question and answer pairs (both the written form and a robot voice speaking those questions and answers). Each topic can be used with all the activities on the site.


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