Question

Find the value of x for {(-2/5)^2}^x*(-5/2)^-1=-8/125

Answer 1

Answer: x=1

Explanation:

`[(-(2)/(5))^2] ^x*(-(5)/(2)) ^(-1)=-(8)/(125) \\\\(-(2)/(5))^(2*x)*(-(2)/(5))^1 =-(2^3)/(5^3) \\\\(-(2)/(5) )^(2x+1)=(-(2)/(5))^3 \\\\Hence,\\\\2x+1=3\\\\2x+1-1=3-1\\\\2x=2`

Divide both parts of the equation by 2:

`x=1`