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Question

By what number should 25 be multiplied so that the product is 1024?
  1. 216
  2. 215
  3. 217
  4. 213


Solution

The correct option is B 215
Let the number be X.
25×X=1024 
 we can write 1024 as 
  210242512225621282642322162824221 
1024=2×2×2×2×2×2×2×2×2×2=210
Now putting 210 in place of 1024
 25×X=210 
X=21025 
Using Laws of Exponents, we know that
aman=amn
X=21025=210(5)=210+5=215  
The number to be multiplied to 25 is 215 to get the product 1024.

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