Question

Simplify the expression with using scientific notation (4 times 10 8)2

Answer 1

The scientific notation:

$a\cdot10^n\\\\1\leq a < 10;\ n\in\mathbb{Z}$

$(4\cdot10^8)^2=4^2(10^8)^2=16\cdot10^{8\cdot2}=16\cdot10^{16}\\\\=1.6\cdot10\cdot10^{16}=1.6\cdot10^{17}$

Used:

$(a\cdot b)^n=a^n\cdot b^n\\\\(a^n)^m=a^{n\cdot m}\\\\a^n\cdot a=a^{n+1}$

Answer: (4 × 10⁸)² = 1.6 × 10¹⁷