Question

What is the value of this expression when a=3 and b=-2?23a^- 2^62a^- 16^5

Answer 1

First, we need to know the following properties:

`\begin{gathered} x^(-a)=(1)/(x^a)^{} \\ (x^a)/(x^b)=x^(a-b) \end{gathered}`

Then, we can rewrite the expression as:

`\begin{gathered} ((3\cdot a^(-2)\cdot b^6)/(2\cdot a^(-1)\cdot b^5))^2=((3)/(2)\cdot a^(-2-(-1))\cdot b^(6-5))^2 \\ ((3\cdot a^(-2)\cdot b^6)/(2\cdot a^(-1)\cdot b^5))^2=((3)/(2)a^(-1)\cdot b^1)^2 \\ ((3\cdot a^(-2)\cdot b^6)/(2\cdot a^(-1)\cdot b^5))^2=((3b)/(2a))^2 \\ ((3\cdot a^(-2)\cdot b^6)/(2\cdot a^(-1)\cdot b^5))^2=(9b^2)/(4a^2) \end{gathered}`

Now, we can replace a by 3 and b by -2 and get:

`(9b^2)/(4a^2)=(9\cdot(-2)^2)/(4\cdot(3)^2)=(9\cdot4)/(4\cdot9)=1`

Answer: 1