Question

Write the following in scientific notation: $(200{)}^3$

• A. $4\times {10}^4$
• B. $8\times {10}^6$
• C. $6\times {10}^6$
• D. $8\times {10}^8$

Answer 1

Answer: (B)

The correct option is B $(8\times {10}^6)$

Given $(200{)}^3=(2\times 100{)}^3$
Using the rule of $(a\times b{)}^m=a^m\times b^m$
$\Rightarrow (200{)}^3=(2{)}^3\times (100{)}^3$
$=2^3\times ({10}^2{)}^3$ [Since, $100={10}^2$]
$=2^3\times {10}^{2\times 3}$ [Since, $(a^m{)}^n=a^{(m\times n)}$]
$=8\times {10}^6$
$\therefore (200{)}^3=8\times {10}^6$