Ejercicios sección 2.1

En los ejercicios 1 a 10 resuelva las operaciones indicadas y simplifique.

1. $\hspace{0.1cm}\cfrac{16\cdot\left(\frac{5^3}{4^3}\right)^{\frac{1}{3}}+8\cdot\left(\frac{2^{-4}}{3^{-4}}\right)^{\frac{1}{4}}}{2^5}\\[0.2cm]$
2. $\hspace{0.1cm}\left(\frac{3}{2}\right)^3\cdot\left[\left(\frac{4}{3}\right)^2\right]^{-2}\cdot \frac{2^{12}}{3^7}\\[0.2cm]$
3. $\hspace{0.1cm}3\left[\left(2\times3\right)^{-1}\cdot\frac{1}{2^3}\right]^{-1}\cdot\left(3\times2^2\right)^{-2}\\[0.2cm]$
4. $\hspace{0.1cm}\left[3-5\cdot\left(\frac{3^2}{2}\right)^{-1}\cdot\frac{3^2}{2}\right]^6\\[0.2cm]$
5. $\hspace{0.1cm}\left\{\left(\frac{2}{5}\right)^2\cdot\left[\left(\frac{6}{2}\right)^2\left(\frac{2}{3}\right)^{-1}\right]^{-1}\right\}^{-1}\\[0.2cm]$

6. $\hspace{0.1cm}\cfrac{\left\{\left(\frac{2}{5}\right)^2\cdot\left[\left(\frac{6}{2}\right)^2\left(\frac{2}{3}\right)^{-1}\right]^{-1}\right\}^{-1}\times\left[3-5\cdot\left(\frac{3^2}{2}\right)^{-1}\cdot\frac{3^2}{2}\right]^6}{5^3\cdot\left(\frac{2^3}{10}\right)}$
7. $\hspace{0.1cm}\left[\cfrac{\left(6\times\frac{1}{3}\div2\right)^{-1}}{\left(\frac{7}{2}\right)^{-1}\cdot\left(\frac{2}{4}\right)^{-2}}\right]^{-2}\\[0.2cm]$
8. $\hspace{0.1cm}\cfrac{m^2\cdot\left(2^3\times n^{-2}\right)}{\left[\left(\frac{m}{2}\right)^3\right]^{-2}}-2\left[\cfrac{n}{\left(m^2\times 2^{-1}\right)^2}\right]^{-2}\\[0.2cm]$
9. $\hspace{0.1cm}\left(\cfrac{2^3}{x^2}\div\cfrac{y^3}{3^2}\right)^{-2}\div\left[\left(\cfrac{y^3}{x^2}\right)^{-1}\div\left(\cfrac{1}{z^{-1}}\right)\right]^{-1}\\[0.2cm]$
10. $\hspace{0.1cm}\cfrac{\left[\cfrac{\left(6\times\frac{1}{3}\div2\right)^{-1}}{\left(\frac{7}{2}\right)^{-1}\cdot\left(\frac{2}{4}\right)^{-2}}\right]^{-2}}{\left[3-5\cdot\left(\frac{3^2}{2}\right)^{-1}\cdot\frac{3^2}{2}\right]^6}\\[0.2cm]$