Hello!
The first thing you should notice is that the exponent will be less than 1, as raising 27 to any power greater than 1 will make it larger, and you're trying to figure out what makes it equal to 3, a number less than 27.
Raising a number to a fractional power is taking its nth root: [tex] 21^{1/3} [/tex] is [tex] \sqrt[3]{21} [/tex], so you'll really need to take the nth root of 27 to get 3. To figure out which root, write the number in exponential form with a base of 3:
[tex] 27^{x} [/tex] = 3
[tex] 3^{3x} [/tex] = [tex] 3^{1} [/tex]
Now, the bases are the same (they are both 3), so you can set the exponents equal to each other:
3x = 1
Divide both sides by 3 and you've isolated x:
[tex]x = \frac{1}{3} [/tex]
Answer:
[tex] 27^{1/3} = 3[/tex]
