Question

Simplify. sal 63 - 3 3b a - 5 Write your answer using only positive exponents.

Answer 1

At first note the following :

`\begin{gathered} a^(-m)=(1)/(a^m) \\ (a^m)^n=a^(m\cdot n) \\ (a^m)/(a^n)=a^(m-n) \\ a^m\cdot a^n=a^(m+n) \end{gathered}`

So, for the given expression :

`\begin{gathered} ((5\cdot a^(-1)\cdot b^3)/(3\cdot b^(-3)\cdot a^(-5)))^(-2) \\ \\ =((5)/(3)\cdot a^(-1--5)\cdot b^(3--3))^(-2) \\ \\ =((5)/(3)\cdot a^4\cdot b^6)^(-2) \\ \\ =((5)/(3))^(-2)\cdot(a^4)^(-2)\cdot(b^6)^(-2) \\ \\ =((3)/(5))^2\cdot a^(-8)\cdot b^(-12) \\ \\ =(9)/(25)\cdot(1)/(a^8)\cdot(1)/(b^(12)) \\ \\ \\ =(9)/(25a^8b^(12)) \end{gathered}`