a)
2^a=\frac{1}{4}
2^a=(\frac{1}{2})^2
2^a=2^{-2}
a=-2
2^{-2}=\frac{1}{4}
b)
(\frac{1}{3})^b=27
(\frac{1}{3})^b=3^3
(\frac{1}{3}^b=(\frac{1}{3})^{-3}
b=-3
(\frac{1}{3})^{-3}=27
c)
(0,1)^c=1000
(\frac{1}{10})^c=10^3
(\frac{1}{10}^c=(\frac{1}{10})^{-3}
c=-3
(0,1)^{-3}=1000
d)
(0,2)^d=25
(\frac{2}{10})^d=25
(\frac{1}{5})^d=5^2
(\frac{1}{5})^d=(\frac{1}{5})^{-2}
d=-2
(0,2)^{-2}=25
e)
(-2)^e= -\frac{1}{32}
(-2)^e=(-\frac{1}{2})^5
(-2)^e=(-2)^{-5}
e=-5
(-2)^{-5}= -\frac{1}{32}
f)
0,25^f=16
(\frac{25}{100})^f=16
(\frac{1}{4})^f=4^2
(\frac{1}{4})^f=(\frac{1}{4})^{-2}
f=-2
0,25^{-2}=16
g)
1000^g=0,001^3
1000^g=(\frac{1}{1000}^3
1000^g=1000^{-3}
g=-3
1000^{-3}=0,001^3
h)
25^{-2}=(\frac{1}{625})^h
(\frac{1}{25})^{2}=(\frac{1}{625})^h
(\frac{1}{625})^1=(\frac{1}{625})^h
h=1
25^{-2}=(\frac{1}{625})^1