index notation

LAW OF INDICES

by cikgu mas

 $a^{m\ \ }\times\ a^{n\ \ }=\ a^{m+n}$  

EXAMPLE : 

 $2^{3\ }\times2^4\ =2^{3+4\ }$  

 $5^7\ \times5^{3\ }\ =5^{7+3}$  

 $11^{21}\ \times11^5\ =11^{21+5}$  

QUESTION :

Simplify each of the following .

a )  $7^2\ \times7^3$  

b)  $\left(0.2\right)^2\ \times\ \left(0.2\right)^4\ \times\left(0.2\right)^5$  

c)  $2k^2\ \times4k^7$  

d)  $3m^{4\ }\times\frac{1}{6}m^8\ \times12m$  

Solution :

a )  $7^2\ \times7^3$  

 $=7^{2\ +3}$  

 $=7^5$  

b)  $\left(0.2\right)^2\ \times\left(0.2\ \right)^4\ \times\left(0.2\ \right)^5$  

 $=\left(0.2\right)^{2+4+5}$  

 $=\left(0.2\ \right)^{11}$  

c ) $2k^2\ \times4k^7$  

 $=\left(2\ \times4\ \right)\ \left(k^2\ \times\ k^7\right)$  

 $=8k^{2\ +7}$  
 $=8k^9$  

d )  $3m^4\ \times\frac{1}{6}m^8\ \times12m$  

 $=\left(3\times\frac{1}{6}\ \times12\right)\left(m^4\ \times m^8\ \times m^1\right)$ 

 $=6m^{4+8+1}$  
 $=6m^{13}$  
  

thats all...

thank you and good luck!!!!!!