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:

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

So we have:

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