Simplify the following exponential expression. Show your work step by step and list the Properties of Exponents used to solve this problem next to your work.
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3x^0 (2x^3y^2)^4
--------------------------
(4x^7y^4) ^2
= 3 * 1 (2x^3y^2)^4
-------------------------- Zero Exponent Property X^0 =1
(4x^7y^4) ^2
3 (2^4 *x^3*4 y^2*4)
-------------------------- power of a power property x^a ^b = x^(a*b)
4^2 x^7*2 y^4*2
3 *16 *x^12 y^8
-------------------------- simplify
16 x^14 y^8
3 *x^12 y^8
-------------------------- simplify
x^14 y^8
3 *x^(12-14) y^(8-8)
-------------------------- Quotient of Power X^a/ X^b = X^ (a-b)
3x^-2 y^0 simplify
3x^-2 *1 Zero Exponent Property X^0 =1
3 / x^2 Negative exponent property x^-a = 1/x^a