Question

Choose the correct option for the scientific notation of $(300{)}^4.$

• A. $81\times {10}^8$
• B. $8.1\times {10}^9$
• C. $810\times {10}^7$
• D. $0.81\times {10}^{10}$

Answer 1

The correct option is B $8.1\times {10}^9$

Let's start by simplifying the given number, $(300{)}^4.$

$(300{)}^4$
$=(3\times 100{)}^4$ $(\because 300=3\times 100)$

$=(3\times {10}^2{)}^4$ $(\because 100=10\times 10={10}^2)$

$=3^4\times ({10}^2{)}^4$ $[\because (a\times b{)}^n=a^n\times b^n]$

$=81\times {10}^{2\times 4}$
$[\because (a^m{)}^n=a^{m\times n}\Rightarrow ({10}^2{)}^4={10}^{2\times 4}\text{and}{3}^4=\underset{–}{3\times 3}\times \underset{–}{3\times 3}=9\times 9=81]$

$=81\times {10}^8$

To write $81.0\times {10}^8$ in scientific notation form, we need to move decimal point one place to the left.

$=8.10\times {10}^1\times {10}^8$
$=8.1\times {10}^{(1+8)}$ $(\because a^m\times a^n=a^{m+n})$
$=8.1\times {10}^9$

$\therefore 8.1\times {10}^9$ is the scientific notation form of $(300{)}^4$.

Hence, option (b.) is the correct one.

Notes:

The scientific notation of a number looks like:


Where

• $1\le A<10$
• $B:$
  • Positive integer equals to the number of places decimal point moves towards left
  • Negative integer equals to the number of places decimal point moves towards right