The answer is [tex] a = 7, b = 9, c = 4 [/tex]
Rational exponents works as follow: considering [tex] a^{\frac{b}{c}} [/tex], the numerator has the role of the usual, whole-number exponents, while the denominator is the order of the root we want to extract. So, again, the writing [tex] a^{\frac{b}{c}} [/tex] means that we want to consider the c-th root of [tex] a^b [/tex], i.e.
[tex] a^{\frac{b}{c}} = \sqrt[c]{a^b} [/tex]
So, in your case, the exponent is nine over four. It means that you want to consider the fourth root of [tex] 7^9 [/tex], hence the answer.
