Question

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

Answer 1

2/5 ^13 is your answer!!!

Answer 2

The required answer is ⅖¹³.

Explanation:

Given terms to us is :-

`=\bf (2)/(5)^8 * (2)/(5)^(-2)* (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 = (2)/(5)^8 * (2)/(5)^(-2)* (5)/(2)^(-7) \\\\\bf= (2)/(5)^8 * (2)/(5)^(-2)* (2)/(5)^7 \\\\\bf= \bigg((2)/(5)\bigg)^((8+7-2))\\\\\boxed{\red{\bf= (2)/(5)^(13)}}`