Question

How do you simplify $8{{x}^{5}}.8{{x}^{7}}$ ?

Answer 1

Hint: Here we have been asked to simplify the given expression $8{{x}^{5}}.8{{x}^{7}}$ for that we will perform some basic arithmetic simplifications and reduce the expression. We will also express it in a very simple way. We will show a method which is time convenient. By performing multiplication operation we can simply write the given expression as $\Rightarrow 8{{x}^{5}}.8{{x}^{7}}=64{{x}^{5+7}}$ and we will further simplify this to get our answer.

Complete step by step solution:
For answering this question we need to simplify $8{{x}^{5}}.8{{x}^{7}}$ .
For simplifying the given expression we will perform simple basic arithmetic calculations and reduce it into a simplified form.
Here initially we will perform simple arithmetic multiplications between the numbers present in the given expression. After multiplying them we will have $8{{x}^{5}}.8{{x}^{7}}=64{{x}^{5+7}}$ .
Now we will add the numbers in the exponents, that is we will perform simple basic arithmetic addition between the numbers five and seven in order to simplify the given expression. After performing the simple basic arithmetic addition between the numbers present in the exponents in the expression we will have $\Rightarrow 8{{x}^{5}}.8{{x}^{7}}=64{{x}^{5+7}}=64{{x}^{12}}$ .
Therefore we will conclude that the given expression can be simply expressed as $8{{x}^{5}}.8{{x}^{7}}=64{{x}^{12}}$ .
This expression can be further simply expressed as $8{{x}^{5}}.8{{x}^{7}}=64{{x}^{12}}\Rightarrow {{\left( 2{{x}^{2}} \right)}^{6}}$ because the value of two to the power six is sixty four.

Note: Here the question which we have answered is very simple and time efficient. There are very less possibilities of mistakes in questions of this type. Similarly we can simplify any expression in mathematics for example for the expression it can be simply expressed as $6{{m}^{3}}.6{{m}^{2}}=36{{m}^{5}}$ .