Question

(2/5) ^ - 4 * (2/5) ^ (2 + x) = 8/125​

Answer 1

Answer:

The value of x has been found to be 5.

Step-by-step explanation:

Here we have been stated above here is the question that we need to calculate the respective value of x from the suggested equation. First of all, we will work out the exponential forms, and then compare the RHS and the LHS bases with the powers as below:

Here we have been mentioned:

$\frac{2}{5} ^{-4} * \frac{2}{5} ^{2 + x} = \frac{8}{125}$

⇒ $\frac{2}{5} ^{-4 + 2 + x} = \frac{2}{5} ^{3}$

⇒ Now we are comparing the LHS and RHS powers as they have exact same base,

⇒  - 4 +2 + x = 3

⇒ -2 + x = 3

⇒ x = 3 + 2

⇒ x = 5

Therefore the value of x is 5.