Question

The expression (a3)2 can be simplified as shown here:

Answer 1

Given expression $(a^3)^2$.

Let us simplify step by step with explaination.

Let us read the given expression.

$(a^3)^2$ 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 2

Answer and Explanation :

Given : The expression $(a^3)^2$ can be simplified as shown here:

$(a^3)^2 = (a^3)(a^3) = (a\cdot a \cdot a)(a \cdot a \cdot a) = a^6$

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 $(a^3)^2$ we have to multiply the term by itself.

So, We can write the term as $(a^3)^2=(a^3)(a^3)$

Step 2 - When we have a cubic term $(a^3)^2$ we have to multiply the term two times by itself.

So, we can write the term as $(a^3)(a^3)= (a\cdot a \cdot a)(a \cdot a \cdot a)$

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 $(a\cdot a \cdot a)(a \cdot a \cdot a)=a^6$

Therefore, following above steps we get,

$(a^3)^2 = (a^3)(a^3) = (a\cdot a \cdot a)(a \cdot a \cdot a) = a^6$