simplify (4xsquaredycubed)(5xpower of -3ypower of -2 z power of 0)

Question

a. 20/xpowerof 6ypowerof6

b. 20x2/y

c. 20xpower of 5 y power of 5

d. 20y/y

Answer 1

(4x²y³  ) (5x^-3 y^-2 z⁰⁾

Rearranging,

= (4*5) x^(2-3) y^(3-2) (1) Note: z⁰ = 1

= 20 x^-1y

= 20y/x

Could you please check d., Appears to be a typo.

Answer 2

     (4x²y³)(5x^-3y^-2z⁰)

First note that anything to the power of 0 is equal to 1....so since z⁰=1, then the expression is now as follows:

               (4x²y³)(5x^-3y^-2) = 4·5·x²·x^-3·y³·y^-2

                                       = 20x²x^-3y³y^-2

When multiplying exponential expressions with like bases, you keep the like base and add the exponents:

          20x²x^-3y³y^-2 = 20x^2+(-3)y^3+(-2)

                             = 20x^2-3y^3-2

                             = 20x^-1y¹

To make the negative exponent positive, move it to the opposite side of the fraction:

          (20x^-1y¹)/1 = (20y¹)/x¹

Whenever the exponent is 1, you don't have to write it out since anything to the power of 1 is itself....so it simplifies to:     20y/x