What's the highest power of $x$ in this nested polynomial?

Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

The highest power of \(x\) in \[\left\{\left[(2x^6+7)^3+(3x^8-12)^4\right]^5 + \left[(3x^5-12x^2)^5+(x^7+6)^4\right]^6\right\}^3\] is

1. \(x^{424}\),

2. \(x^{450}\),

3. \(x^{500}\),

4. \(x^{504}\).

What is the highest power of \(x\) in \((2x^6+7)^3\)? Can we do the same for the other terms?