Question

Need help on number 4 Please help me on my hw

Answer 1

4)

The given expression is,

`((2a^(-1)b)/(a^2b^(-3)))^(-3)`

The above expression can be simplified as,

`((2a^(-1)b)/(a^2b^(-3)))^(-3)=(2^(-3)(a^(-1))^(-3)b^(-3))/((a^2)^(-3)(b^(-3))^(-3))\text{ }\mleft(Since(c^m)^n=c^(mn)\mright)`
`=(2^(-3)a^3b^(-3))/(a^(-6)b^9)`
`\begin{gathered} \\ =\frac{^{}2^(-3)a^(3+6)^{}}{^{}^{}b^(9+3)}\text{ (Since }(c^m)/(c^n)=c^(m-n)) \\ =\frac{^{}2^(-3)a^9}{^{}b^(12)}\text{ } \\ =\text{ }(a^9)/(2^3b^(12))\text{ Since (}c-^m=(1)/(c^m)) \\ =\frac{a^9}{8^{}b^(12)} \end{gathered}`

Therefore , the simplified expression with no negative exponents is,

`\frac{a^9}{8^{}b^(12)}`