Simplify 3⁵x10⁵x25 / 5⁷x6^​5

Please find below the solution to the asked query:

We have : $\frac{3^5 \times {10}^5 \times 25}{5^7 \times 6^5}$ , So

$$\begin{gathered} \Rightarrow \frac{3^5 \times {\left(2 \times 5\right)}^5 \times 5 \times 5}{5^7 \times {\left(2 \times 3\right)}^5} \\ \Rightarrow \frac{3^5 \times 2^5 \times 5^5 \times 5 \times 5}{5^7 \times 2^5 \times 3^5} ( \mathrm{We} \mathrm{know} {\left( \mathrm{a} \times \mathrm{b} \right)}^{\mathrm{m}} = {\mathrm{a}}^{\mathrm{m}} \times {\mathrm{b}}^{\mathrm{m}} ) \\ \Rightarrow \frac{3^5 \times 2^5 \times 5^{5+1+1} }{5^7 \times 2^5 \times 3^5} ( \mathrm{We} \mathrm{know} {\mathrm{a}}^{\mathrm{m}} \times {\mathrm{a}}^{\mathrm{n}} = {\mathrm{a}}^{\mathrm{m}+\mathrm{n}} ) \\ \Rightarrow \frac{3^5 \times 2^5 \times 5^7 }{5^7 \times 2^5 \times 3^5} \\ \mathbf{\Rightarrow }\mathbf{1}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)} \end{gathered}$$

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