If #5^(-x) = 3#, what does #5^(3x)# equal?

2 Answers
Jan 14, 2017

#5^-x=3 rArr 1/5^x=3 rArr 5^x=1/3#
#:." Reqd. Value ="5^(3x)=(5^x)^3=(1/3)^3=1/27#.

Jan 15, 2017

#5^(3x)=1/27#

Explanation:

Another approach:

Recall that #(a^b)^c=a^(bc)#. So, if we currently know #5^-x# and want to determine #5^(3x)#, we see their powers are off by a factor of #-3#. Thus, we can write:

#5^(3x)=(5^-x)^(-3)#

Which is useful because we know #5^-x=3#, so:

#5^(3x)=3^-3#

Using the rule #a^-b=1/a^b# this becomes:

#5^(3x)=1/3^3=1/27#