1.if 1/5^3y=0.008,then find the value of 0.25^y

Taking log on both sides we have

3y log(1/5) = log (0.008)

we can write 

3y log(0.2) = log(0.23) or 3 log(0.2)

3y log(0.2) =3 log(0.2)

solving we get y = 1

hence 

0.25y = 0.251 = 0.25

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(1/5)3y=0.008

=> (1/5)3y=8/1000

=> (1/5)3y=(2/10)3

=> (1/5)3y=(1/5)3

now bases are same therefore powers are equal

=> 3y=3

=> y=1

now value of (0.25)y=(0.25)1=0.25

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