Simplify and write the equation with positive exponents

Question

(2xy³)^-2

Answer 1

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 = a^n+(-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)         

Answer 2

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)