Question

Which shows how to find the value of this expression when x=-2 and y=5?
(3x^3y^-2)2

Answer 1

Put x = -2 and y = 5 to the expression.

`(3x^3y^(-2))^2`

`\left[3\cdot(-2)^3(5)^(-2)\right]^2=\left[3(-8)\cdot(1)/(5^2)\right]^2=\left(-24\cdot(1)/(25)\right)^2=\left(-(24)/(25)\right)^2\\\\=(24^2)/(25^2)=(576)/(625)`

Step-by-step explanation

`(-2)^3=(-2)(-2)(-2)=-8\\\\a^(-n)=(1)/(a^n)\to5^(-2)=(1)/(5^2)=(1)/((5)(5))=(1)/(25)\\\\a^2\geq0\ \text{for any real number}\to\left(-(24)/(25)\right)^2=\left((24)/(25)\right)^2\\\\\left((a)/(b)\right)^2=(a^2)/(b^2)\to\left((24)/(25)\right)^2=(24^2)/(25^2)=((24)(24))/((25)(25))=(576)/(625)`