Question

Por favor ayuda plis es urgente

Answer 1

Para resolver los ejercicios tendremos en cuenta las propiedades exponenciales. Y la factorización de polinomios.

1.  

     $(\frac{3}{5})^{4} = \frac{3^{4}}{5^{4}}=\frac{81}{625}$

2.  

     $(\frac{5}{2})^{2} * (\frac{5}{2})^{3} = (\frac{5}{2})^{2+3}=(\frac{5}{2})^{5}= \frac{3125}{32}$

3.  

     $[(\frac{1}{3} )^{10}+(\frac{1}{3} )^{7}]^{2} = [\frac{1}{3^{10}}+\frac{1}{3^{7}}]^{2} =\\***T.C.Perfecto.: (a+b)^{2}=a^{2}+2ab+b^{2} \\(\frac{1}{3^{10}})^{2}+2*\frac{1}{3^{10}}*\frac{1}{3^{7}}+(\frac{1}{3^{7}})^{2}=\frac{1}{3^{20}}+\frac{2}{3^{17}}+\frac{1}{3^{14}}$

     **Queda a tu criterio el realizar o no la suma de fracciones.

4.  

     $(\frac{2}{3})^{2} * (\frac{2}{3})^{3} = (\frac{2}{3})^{2+3}=(\frac{2}{3})^{5}=(\frac{2^{5}}{3^{5}})=\frac{32}{243}$

5.  

     $[(\frac{2}{3}) ^{2}]^{3}= (\frac{2}{3}) ^{2*3}=(\frac{2}{3}) ^{6}=(\frac{2^{6}}{3^{6}})= \frac{64}{729}$

6.  

     $\frac{(\frac{3}{4})^{5} * (\frac{3}{4})^{-2} }{(\frac{3}{4})^{-1} * (\frac{3}{4})^{6}} = \frac{(\frac{3}{4})^{5+(-2)}}{(\frac{3}{4})^{-1+6}} = \frac{(\frac{3}{4})^{3}}{(\frac{3}{4})^{5}}=\\***Simplificar--->(Numerador/Denominador)\\\frac{1}{(\frac{3}{4})^{2}} = \frac{1}{(\frac{3^{2}}{4^{2}})} = \frac{1}{(\frac{9}{16})}= \frac{16}{9}}$

7.  

      $\frac{(\frac{2}{5})^{8} * (\frac{2}{5})^{-3} }{((\frac{2}{5})^{-1} * (\frac{2}{5})^{10})^{2}} = \frac{(\frac{2}{5})^{8+(-3)}}{((\frac{2}{5})^{-1+10})^{2}}=\frac{(\frac{2}{5})^{5}}{((\frac{2}{5})^{9})^{2}}=\frac{(\frac{2}{5})^{5}}{(\frac{2}{5})^{9*2}}=\frac{(\frac{2}{5})^{5}}{(\frac{2}{5})^{18}}\\*** Simplificar ---> (Numerador/Denominador)\\(\frac{1}{(\frac{2}{5})^{13}})$

      **Este último valor no lo continúes a no ser que explícitamente te lo exijan. Es largo.