Question

How do you simplify $ 3{{a}^{2}}\cdot 3a $ ?

Answer 1

Hint: In this question, we need to simplify $ 3{{a}^{2}}\cdot 3a $ . For this, we will multiply both 3's separately and variables separately. We will use the commutative property to arrange the terms first. Then we will apply the property of the exponent to solve the variable part. According to property of exponents $ {{x}^{m}}\cdot {{x}^{n}}={{x}^{m+n}} $ .

Complete step by step answer:
Here we are given the expression as $ 3{{a}^{2}}\cdot 3a $ .
We need to simplify it as much as possible. We can say that we have four terms here, 3, a, 3, $ {{a}^{2}} $ . all are multiplied. Since we know that, multiplication is commutative i.e. ab = ba, so we can rearrange the order of multiplication.
 $ 3{{a}^{2}}\cdot 3a $ can be written as $ 3\cdot 3\cdot {{a}^{2}}\cdot a $ (We have changed order of $ {{a}^{2}} $ and 3).
Now we can multiply the terms (which are possible) to get a simplified answer. We know $ 3\times 3 $ is equal to 9 so, $ 3\cdot 3=9 $ we get $ 9{{a}^{2}}\cdot a $ .
Since both variables is in terms of a, so they can also be simplified. Exponent of a can be written as 1 so, our expression becomes $ 9{{a}^{2}}\cdot {{a}^{1}} $ .
Now let us apply the property of exponents according to which the power of terms with same base are added if terms are multiplied i.e. $ {{x}^{m}}\cdot {{x}^{n}}={{x}^{m+n}} $ . Here x = a, m = 2 and n = 1 so we get $ 9{{a}^{2+1}}\Rightarrow 9{{a}^{3}} $ .
Hence our expression becomes $ 9{{a}^{3}} $ .
This expression cannot be simplified further. Therefore our required answer is $ 9{{a}^{3}} $ .

Note:
 Students should keep in mind all the properties of exponents, before solving this sum. Students could also split $ {{a}^{2}} $ into $ a\times a $ and then write $ 9\times a\times a\times a $ . Since $ x\times x\times x={{x}^{3}} $ . So they could write $ 9{{a}^{3}} $ which is the same answer. Make sure that base of exponential terms is the same before applying this property. Note that here '.' between 3's denote multiplication and not decimal.