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

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asked Dec 1, 2023 129k views

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

Mathematics
high-school

Gordon Henriksen asked

by Gordon Henriksen

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1 Answer

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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

Robmcm answered Dec 5, 2023

by Robmcm

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