EXPONENTIALS K1

 

If 5^2w (40^w) = (0.000001)²⁰ ; Find w.

 

Solution

 

5^2w (40^w) = (0.000001)²⁰ ;

 

(5²)^w (40^w) = (10^-6)²⁰ ;

 

(25)^w (40^w) = 10^{-6 x 20} ;

 

(25 x 40)^w = 10^-120

 

(1000)^w = 10^-120

 

(10³)^w = 10^-120

 

10^3w = 10^-120   (Bases are alike, so they cancel out)

 

3w = -120

 

3w = -120^-40

3         3

 

w = -40 answer

 

TRY THIS…………………………   

 

If 4^2a (2^a) = 128 ; Find a.