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