TANCET 2013 Quant Qn 3: Indices

Step by step solution

1. (0.004 * 10^a)(0.32 * 10^b) = 128 * 10³
2. We can write 0.004 as
   
   Similarly, we can write 0.32 as
   
   
3. So, the expression can be rewritten as ( * 10^a)( * 10^b) = 128 * 10³
   
   
4. Or = 128 * 10³
   
   
5. i.e., = 128 * 10³
   
   
6. i.e., 128 * 10^{a + b - 5} = 128 * 10³
   
   
7. Dividing both sides by 128, we get 10^{a + b - 5} = 10³
   
   
8. As the bases are equal, we can equate the indices.
   a + b - 5 = 3
   Or a + b = 8
   
   

  The correct answer is Choice 4. (a + b) = 8

Remember these Rules of Indices

1. a^x * a^y = a^{x + y}
   
   
2. (a^x)^y = a^xy
   
   
3. = a^{x - y}
   
   
4. 
   
   e.g.,
   
   
5. a^-x =
   
   
6. a^x * b^x = (a*b)^x