Question

for what value of a will 4 x. 10^6 be times larger than a x 10^5

Answer 1

Interpretation: "4×10^6 is a times larger than a×10^5" means
4×10^6 = a·(a×10^5) = a^2·10^5.

Solve:
a^2·10^5 = 4·10^6
a^2 = 4·10^6 / 10^5 = 40
a = ±√40 = ±2√10 ≈ ±6.3249.

Since "times larger" normally refers to a positive factor, a = 2√10 ≈ 6.3249.