Question

Describe the Method and Operation

Answer 1

`\text{Answer: 5n}^8m^6`

Given that

`\begin{gathered} ((5n^6)/(m^(-3)n^2))^2 \\ \text{According to the law of indies,} \\ ((a)/(b))^2\text{ = }((a)^2)/((b)^2) \\ ((5n^6)/(m^(-3)n^2))\text{ = }((5n^6)^2)/((m^(-3)n^2)^2) \\ \text{According to the law of indicies again,} \\ (a^x)^y=a^(x\cdot y) \\ =\text{ }\frac{(5n^{6\text{ x 2}})}{(m^(-3\cdot2)n^(2\cdot2))} \\ =\text{ }(5n^(12))/((m^(-6)n^4)) \\ \text{According to the law of indices} \\ x^(-1)\text{ = }(1)/(x) \\ =5^{}n^(12)\cdot n^(-4)\cdot m^6 \\ =5n^{12\text{ - 4}}m^6 \\ =5n^8m^6 \end{gathered}`