Question

Simplify the following in exponential form $${\left({\displaystyle \frac{5}{2}}\right)}^6\times {\left({\displaystyle \frac{5}{2}}\right)}^2$$ .

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
$$\begin{array}{l}a={\displaystyle \frac{5}{2}}\\ x=6\\ y=2\end{array}$$
Now putting all of this in the property of exponentials we will get it as
$$\begin{array}{l}\therefore {\left({\displaystyle \frac{5}{2}}\right)}^6\times {\left({\displaystyle \frac{5}{2}}\right)}^2={\left({\displaystyle \frac{5}{2}}\right)}^{6+2}\\ \Rightarrow {\left({\displaystyle \frac{5}{2}}\right)}^6\times {\left({\displaystyle \frac{5}{2}}\right)}^2={\left({\displaystyle \frac{5}{2}}\right)}^8\end{array}$$
So we are getting the final answer as $${\left({\displaystyle \frac{5}{2}}\right)}^8$$

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.