Negative exponents and scientific notation

Question

1/2^-4 

 

is the question. Since the 2 is a negative exponent does that mean it goes on top? 

Answer 1

You should have written as 1/( 2^-4 ) not to get confused by ( 1/2) ^-4

 

 

 1/ 2^-4 = 1 * 2 ⁴ = 16

 

( 1/2 ) -4 =  1/ ( 2 ^-4 ) = 1* 2^4 = 16

 

  Here since the numerator is 1 , doesn't effect the answer:

 

  But  for

 

    2/( 3^{- 4} ) = 2 * 3 ⁴  = 2  * 81 = 162

 

    (2/3 ) ^-4  = (1/2⁴ ) * 3^4 = 81/16 

    

    So you have to place the parenthesis properly. Any negative exponent equals a positive exponent of its    reciprocal.