Question

(2/5)^8 x (2/5)^-2 / (5/2)^-7

Answer 1

2/5 ^13 is your answer!!!

Answer 2

Answer:

The required answer is ⅖¹³.

Step-by-step explanation:

Given terms to us is :-

$=\bf \dfrac{2}{5}^8 \times \dfrac{2}{5}^{-2}\times \dfrac{5}{2}^{-7}$

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 ,

$\bf = \dfrac{2}{5}^8 \times \dfrac{2}{5}^{-2}\times \dfrac{5}{2}^{-7} \\\\\bf= \dfrac{2}{5}^8 \times \dfrac{2}{5}^{-2}\times \dfrac{2}{5}^7 \\\\\bf= \bigg(\dfrac{2}{5}\bigg)^{(8+7-2)}\\\\\boxed{\red{\bf= \dfrac{2}{5}^{13}}}$