Respuesta :
Given expression [tex](a^3)^2[/tex].
Let us simplify step by step with explaination.
Let us read the given expression.
[tex](a^3)^2[/tex] could be read as a power 3 and whole power 2.
Because we have whole power 2 of a^3. That represents two factors of (a^3) is there. So, we could write two factors of a^3 as (a^3)(a^3).
So, first step is (a^3) (a^3).
Now, each of the factor has a^3.
That is read as a power 3, that is three factors of a.
So, we can write a^3 in expanded form as a*a*a.
For each a^3, we would write a*a*a.
We have two facrors of a^3 there.
So, (a^3)(a^3) could be written as (a*a*a)(a*a*a).
There are 3+3=6 factors of a's there.
So, we could rewrite (a*a*a)(a*a*a) as 6 power of a.
That is a^6.
Therefore, we got the steps :
(a^3)^2 = (a^3)(a^3) = (a*a*a)(a*a*a) = a^6.
Answer and Explanation :
Given : The expression [tex](a^3)^2[/tex] can be simplified as shown here:
[tex](a^3)^2 = (a^3)(a^3) = (a\cdot a \cdot a)(a \cdot a \cdot a) = a^6[/tex]
To find : Write out in words how you would explain each step of this process to a friend. Why is each step equal to the previous step?
Solution :
Step 1 - When we have a square term [tex](a^3)^2[/tex] we have to multiply the term by itself.
So, We can write the term as [tex](a^3)^2=(a^3)(a^3)[/tex]
Step 2 - When we have a cubic term [tex](a^3)^2[/tex] we have to multiply the term two times by itself.
So, we can write the term as [tex](a^3)(a^3)= (a\cdot a \cdot a)(a \cdot a \cdot a) [/tex]
Step 3 - When we have the same term repeat in multiple six times then the power of the term became 6.
So, we can write its as [tex](a\cdot a \cdot a)(a \cdot a \cdot a)=a^6[/tex]
Therefore, following above steps we get,
[tex](a^3)^2 = (a^3)(a^3) = (a\cdot a \cdot a)(a \cdot a \cdot a) = a^6[/tex]
