Question

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

Answer 1

Hint: To simplify the given expression, first group similar terms (all similar variables in a group or parentheses and constant in other groups) with the help of commutative law of multiplication. Then after grouping the similar variables together and constants together, use law of indices for multiplication to perform multiplication between the similar variables and also perform algebraic operations (if exists in the given equation) with constants to simplify them too with the variable.

Complete step by step solution:
In order to simplify the given expression $2a \times {a^2}$ we will first group similar terms in the given expression with the help of commutative property of multiplication as follows
$\Rightarrow 2 \times \left( {a \times {a^2}} \right)$
Now, we will use the law of indices for multiplication in order to multiply the similar variables present in the expression. Law of indices for multiplication is given as when “x” to the power of “m” is being multiplied with “x” to the power of “n”, then their product is given as “x” to the power of sum of “m” and “n”, mathematically it can be understood as follows
${x^m} \times {x^n} = {x^{m + n}}$
Using this for the above expression we will get
$
  \Rightarrow 2 \times \left( {a \times {a^2}} \right) \\
   \Rightarrow 2 \times {a^{1 + 2}} \\
   \Rightarrow 2{a^3} \\
 $
Therefore $2{a^3}$ is the simplified form of the expression $2a \times {a^2}$

Note: If a variable or a number is written without exponents then it should be automatically considered that the power of that number or variable is equal to one, as we have considered in this question, you can see we have written $a \times {a^2} = {a^{1 + 2}}$ which says that the power of a is equal to one.