Question

Simplify the following in exponential form \[{\left( {\dfrac{5}{2}} \right)^6} \times {\left( {\dfrac{5}{2}} \right)^2}\] .

Answer 1

Hint: We know that the formula of exponential form is \[{a^x} \times {a^y} = {a^{x + y}}\] . Use this property of exponentials to solve the given question.
Complete step by step answer:
We know that \[{a^x} \times {a^y} = {a^{x + y}}\] Here for this question
\[\begin{array}{l}
a = \dfrac{5}{2}\\
x = 6\\
y = 2
\end{array}\]
Now putting all of this in the property of exponentials we will get it as
\[\begin{array}{l}
\therefore {\left( {\dfrac{5}{2}} \right)^6} \times {\left( {\dfrac{5}{2}} \right)^2} = {\left( {\dfrac{5}{2}} \right)^{6 + 2}}\\
 \Rightarrow {\left( {\dfrac{5}{2}} \right)^6} \times {\left( {\dfrac{5}{2}} \right)^2} = {\left( {\dfrac{5}{2}} \right)^8}
\end{array}\]
So we are getting the final answer as \[{\left( {\dfrac{5}{2}} \right)^8}\]

Note: Don't try to do this by expanding all the terms and then after multiplying all again find the factors. That's a completely wrong process and it's hardly a two marks question so if you won't use this property of exponentials it is possible that you will get a correct answer but that will consume an immense amount of time.