To the power of SIX!

Let $a$ and $b$ be roots of a quadratic equation:

$x^2-4x+7=0$

Find: $a^6+b^6$

Hint:

From a quadratic equation $Ax^2+Bx+C$

Sum of roots of a quadratic equation is $\dfrac{-B}{A}$

Product of roots of a quadratic equation is $\dfrac{C}{A}$