Game: FOUR IN A ROW
Aim: To get four symbols in a row
Method:
Choose a square and click on it. Click on the correct answer to the question in the box that appears. If you are right the square is replaced by a tick. Continue until you have won 4 in a row...
8th grade / Number / Powers & Roots / Indices / Multiply 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.
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
With our Four in a row math game you will be practicing the topic "Multiply indices" from 8th grade / Number / Powers & Roots / Powers & Roots. The math in this game consists of 16 questions that ask you to multiply indices with the same base by adding powers e.g. 5a³ x 6a² = 30a⁵.
The game will reinforce the math you have chosen to learn by getting you to match the question to the correct answer.
Notes
UXO * Duck shoot * The frog flies * Pong * Cat and mouse * The beetle and the bee
Rock fall * Four in a row * Sow grow * Choose or lose * Mix and match
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