Answer:
The required answer is ⅖¹³.
Step-by-step explanation:
Given terms to us is :-
[tex]=\bf \dfrac{2}{5}^8 \times \dfrac{2}{5}^{-2}\times \dfrac{5}{2}^{-7}[/tex]
We can see here that two terms have same base that is ⅖ . And the other is 5/2. So for simplifing the expression we will use some laws of exponents , which are :-
- a ^m + aⁿ = a^{m + n }
- a -ⁿ = ( 1/a )ⁿ
Using these we have ,
[tex]\bf = \dfrac{2}{5}^8 \times \dfrac{2}{5}^{-2}\times \dfrac{5}{2}^{-7} \\\\\bf= \dfrac{2}{5}^8 \times \dfrac{2}{5}^{-2}\times \dfrac{2}{5}^7 \\\\\bf= \bigg(\dfrac{2}{5}\bigg)^{(8+7-2)}\\\\\boxed{\red{\bf= \dfrac{2}{5}^{13}}}[/tex]
