Question

Which of the following is equivalent to the expression (9x^2y^3)(12x^-3y^5)(2xy)?

Answer 1

`\large\boxed{(9x^2y^3)(12x^(-3)y^5)(2xy)=216y^9}\to\boxed{B.}`

Explanation:

`(9x^2y^3)(12x^(-3)y^5)(2xy)=(9\cdot12\cdot2)(x^2x^(-3)x)(y^3y^5y)\\\\\text{Use}\ a^n\cdot a^m=a^(n+m)\\\\=216x^(2+(-3)+1)y^(3+5+1)=216x^0y^9\\\\\text{Use}\ a^0=1\ \text{for any value of}\ a\ \text{except 0}\\\\=216y^9`

Answer 2

`=216y^9`

Explanation:

the expression is:

`(9x^2y^3)(12x^(-3)y^5)(2xy)`

the first step is to multiply all the coefficients:

`9*12*2=216`

and as for the variables, to multiply them we must add the exponents, that is, the result for x will be:

`x^(2-3+1)=x^0=1`

so there will be no x in our result.

adding the exponents for the y variable:

`y^(3+5+1)=y^9`

The result is the multiplied coefficients and the variables after we add the exponents they in the original expression:

`(9x^2y^3)(12x^(-3)y^5)(2xy)`
`=216y^9`

which is option B