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How to solve expanded expressions

Hi im trying to solve 
 
a^8 for homework I really want to know how to solve this.
 
And my next qeustion was how do I sopve (4y^3)^2

2 Answers by Expert Tutors

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Mike S. | Tutor with practical knowledge and resources to help students succeed.Tutor with practical knowledge and resou...
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Hi Raymond-
 
[1] - [a^8] means 'a' raised to the 8th power - which is short-hand for [a*a*a*a*a*a*a*a].
 
[2] - For your second example there - [4y^3]^2 - from the rules for grouping and exponents & powers -
 
this is short-hand for: [4*y^3] * [4*y^3] = ??
 
so if we multiply these terms out - we get: 4^2 * y^6 = 16 * y^6 [ the numbers 4 * 4 will give you 16 and exponents with the same base will ADD [3 + 3 = 6].
 
ANSW = 16y^6
 
Hope this info was helpful..
 
Mike S
Raymond R. | Heyo, I enjoy tutoring anything chemistry related Heyo, I enjoy tutoring anything chemistr...
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Hi Thomas, 
 
Check out the exponent rules if you can, i'm not too clear on what the first part of your question is (a)8? You may need to provide some more information on that 
 
But your second question is all about exponential rules. Remember x3 is the same as (x*x*x)
 
so (x3)2 can be written as (x*x*x)(x*x*x) which is x, know that if a function has an exponent on the outside of the parenthesis you can multiply it, to save time, (x3)2 , 3*2= 6, so x6
 
Looking at your problem, it can written as (4y3)(4y3) which would be equal to 16y6
 
You should definitely check out exponent rules if you can, to clear up any confusion. 
 
Hope this helps you!