Question

Express each of the following numbers using exponential notations:

1. $512$
   
2. $343$
   
3. $729$
   
4. $3125$
   

Answer 1

$\left(i\right)512=(256\times 2)=(16{)}^2\times 2$
$=(2^4{)}^2\times 2$
$=2^8\times 2$
$=2^{(8+1)}$ [Since, $a^m\times a^n=a^{m+n}$]

$\therefore 512=2^9$

(ii) Given $343=7\left(49\right)=7(7{)}^2=7^3$

$\therefore 343=7^3$

$\left(iii\right)729=9\left(81\right)=9(9{)}^2$
$=9^3$
$=(3^2{)}^3$
$=3^6$ [Since, $(a^m{)}^n=a^{m\times n}$]

$\therefore 729=9^3=3^6$

$\left(iv\right)3125=5\left(625\right)$

$=5(25{)}^2$
$=5(5^2{)}^2$
$=5\times 5^4=5^5$

$\therefore 3125=5^5$