If gcd(a,35) = 1, show that $\displaystyle a^12 equiv/ 1$ (mod 35)

the hint in the book says remember, by Femat's thm: $\displaystyle a^6 equiv/1$ (mod 7) and $\displaystyle a^4 equiv/1$ (mod 5)

So since gcd(a,5) = 1 and gcd(a,7) = 1, you can apply Fermat's them - and prove the hint

But thats where I'm stuck - is there another theorem I've forgot where you can multiply the exponent and mod???? is it a property I don't remember??

help!