Question

How do you simplify $\left( {{b}^{8}}{{c}^{6}}{{d}^{5}} \right)\left( 8{{b}^{6}}{{c}^{2}}d \right)$ ?

Answer 1

Hint: In this question, we have to simplify an algebraic expression. Thus, we will use the exponent formula and the basic mathematical rules to get the solution. First, we will open the brackets of the given problem and then collect the like terms together. After that, we will apply the exponent rule, which states that if the bases are the same in multiplication, then their powers are added to each other. Thus, after the necessary calculations, we get the required result for the problem.

Complete step by step solution:
According to the question, we have to simplify the given algebraic expression.
Thus, we will apply the exponent rule to get the solution.
The algebraic expression given to us is $\left( {{b}^{8}}{{c}^{6}}{{d}^{5}} \right)\left( 8{{b}^{6}}{{c}^{2}}d \right)$ ----------- (1)
First, we will open the brackets of term (1), we get
$8{{b}^{8}}{{c}^{6}}{{d}^{5}}{{b}^{6}}{{c}^{2}}d$
Now, we will collect the like terms together, we get
$8\left( {{b}^{8}}{{b}^{6}} \right)\left( {{c}^{6}}{{c}^{2}} \right)\left( {{d}^{5}}d \right)$
Now, we will apply the exponent rule which states that if the bases are the same in multiplication, then their powers are added to each other, that is ${{a}^{x}}{{a}^{y}}={{a}^{x+y}}$ . Therefore, we will apply this formula in the above expression, we get
$8\left( {{b}^{8}}^{+6} \right)\left( {{c}^{6}}^{+2} \right)\left( {{d}^{5+1}} \right)$
On further solving the above expression, we get
$8\left( {{b}^{14}} \right)\left( {{c}^{8}} \right)\left( {{d}^{6}} \right)$
Thus, we cannot simplify the above expression more because we get three variables that are different from each other.

Therefore, for the algebraic expression $\left( {{b}^{8}}{{c}^{6}}{{d}^{5}} \right)\left( 8{{b}^{6}}{{c}^{2}}d \right)$ , its simplified value is $8{{b}^{14}}{{c}^{8}}{{d}^{6}}$ which is the required solution.

Note: While solving this question, do mention all the steps and the rules properly to avoid mathematical errors. Also, do not forget to write 8 in your answer to get an accurate answer to the problem.