Question 192974
1)(1/5)^-7=78125
(5/1)^7=78125
5^7=78125    ok

log to base  5  of  78125=7

checklog78126/log5=7  ok

2) ( (256x^4y)^(1/4))/( (81xy^3)^(3/4))
num
256^.25=4
(x^4)^.25=x^1=x
den
81^(3/4)= (81^.25)^3=3^3=27
(y^3)^(3/4)=(y^(9/4)
combining
( 4*x*y^.25)/ ( 27*x^.75*y^(9/4))
remember  to  divide common  bases,, subst  exponents
(4x^.250/(27y^2)

check,  let  x=2,  y=3
answer  (4*2^.25)/(27*3^2) =.01957
original  ((256*2^4*3)^.25)/( ( 81*2*3^3)^.75)
10.5286/537.85 = .0196  ok


3)  log  base  3  of  27 = x
log27/log3=3=x

check  3^3=27  ok

4)  (y^(2/6))*(y^(-2/6)+8y^(4/6))
y^(2/6-2/6) +8 y^(2/6+4/6)
Y^0 +8y^1
1+8y