Question

What is the value of this expression when a = 3 and b = -2?

Answer 1

The first step: Simplify the expression with:

`(x^n)/(x^m)=x^(n-m)\\\\(xy)^n=x^ny^n\\\\(x^n)^m=x^(nm)\\\\x^(-n)=(1)/(x^n)`

`\left((3a^(-2)b^6)/(2a^(-1)b^5)\right)^2=\left((3)/(2)a^(-2-(-1))b^(6-5)\right)^2=\left((3)/(2)a^(-1)b^1\right)^2\\\\=\left((3)/(2)\right)^2(a^(-1))^2b^2=(9)/(4)a^(-2)b^2=(9b^2)/(4a^2)`

The second step: Put the values of a = 3 and b = -2 to the expression:

`(9(-2)^2)/(4(3)^2)=((9)(4))/((4)(9))=1`

Answer: 1