Question

Simplify the following expression to simplest form using only positive exponents. 4

Answer 1

In order to simplify this expression, we need to use the following properties:

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

So we have:

`\begin{gathered} (49x^(-12)y^(-10))^{-(1)/(2)}\\ \\ =(7^2x^(-12)y^(-10))^{-(1)/(2)}\\ \\ =7^{2\cdot(-(1)/(2))}\cdot x^{-12\cdot(-(1)/(2))}\cdot y^{-10\cdot(-(1)/(2))}\\ \\ =7^(-1)\cdot x^6\cdot y^5\\ \\ =(x^6y^5)/(7) \end{gathered}`