Question

Simplify
(i) 3⁵*10⁵*25
5⁷*6⁵
(ii) 2⁵*3⁴*5
3*16
(iii) 12⁴​*9⁴*4
6³*8^2*27

Answer 1

Dear student
$$\begin{gathered} \mathrm{i})\frac{3^5\times {10}^5\times 25}{5^7\times 6^5} \\ =\frac{3^5\times {\left(2\times 5\right)}^5\times 5^2}{5^7\times {\left(2\times 3\right)}^5} \\ =\frac{3^5\times 2^5\times 5^5\times 5^3}{5^7\times 2^5\times 3^5} \\ =3^{5-5}\times 2^{5-5}\times 5^{5+3-7}\left[\mathrm{As}\frac{{\mathrm{a}}^{\mathrm{m}}}{{\mathrm{a}}^{\mathrm{n}}}={\mathrm{a}}^{\mathrm{m}-\mathrm{n}}\right] \\ =3^0\times 2^0\times 5^1\left[\mathrm{As}{\mathrm{a}}^0=1\right] \\ =5 \end{gathered}$$
similarly, try other parts.
Regards