Question

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

Answer 1

`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`.

Answer 2

`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`