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