Question

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.

Answer 1

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