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
\(x^{424}\),
\(x^{450}\),
\(x^{500}\),
\(x^{504}\).
The highest power of \(x\) in \((2x^6 + 7)^3\) is \(x^{18}\), and in \((3x^8 - 12)^4\) is \(x^{32}\), so in the first square bracket the highest power is \((x^{32})^5 = x^{160}\).
Similarly, the highest power of \(x\) in \((3x^5 - 12x^2)^5\) is \(x^{25}\), and in \((x^7 + 6)^4\) is \(x^{28}\), so in the second square bracket the highest power is \((x^{28})^6 = x^{168}\).
So overall, the highest power of \(x\) in the expansion is \((x^{168})^3 = x^{504}\), and the answer is (d).
