Question

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

Answer 1

Answer:

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

Step-by-step 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

Answer:

$=216y^9$

Step-by-step 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