Question

If 64 x 625 = 2^a x 5^b ; find:  the values of a and b.

Answer 1

the values of a and b.

64 x 625 = 2^a x 5^b 

64 = 2^a 

2	64
2	32
2	16
2	8
2	4
2	2
	1

 

 

 

 

 

 

 

64 = 2 × 2 × 2 × 2 × 2 × 2

64 = 2⁶  

∴ a = 6 

Also, 625 = 5^b

5	625
5	125
5	25
5	5
	1

 

 

 

 

 

625 = 5 × 5 × 5 × 5

625 = 5⁴ 

∴ b = 4