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Simplify and write the equation with positive exponents

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2 Answers

To make a negative exponent positive, move the base and its exponent to the opposite location in the fraction (reciprocation). That is,   a-n = 1/an   and   1/a-n = an.

Using the laws of exponents, we can prove the above by the following:

      an • a-n = an+(-n) = a0 = 1 ;  therefore,  a-n = 1/an (where a≠0). 

With this,    (2xy3)-2 = 1/(2xy3)2 

               1/(2xy3)2 = 1/(22x2(y3)2)

                             = 1/(4x2y6)         

A negative exponent means that you take the reciprocal of what is being raised to the power. For example,

x-1 = 1/x
(1/y)-2 = y2

That being said, (2xy3)-2 = 1/(2xy3)2 or 1/(4x2y6)