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Need help on number 4 Please help me on my hw

Need help on number 4 Please help me on my hw-example-1
User Huan Zhang
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1 Answer

6 votes

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)}

User Jrmgx
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