Question

Aplica las propiedades de la potenciación y simplifica las siguientes expresiones:
a. 3^2×3^2×3^1= ____3^(2+2+1)=3^5=343______________
b. 7^8÷7^6= ______________________________________________
c. 〖〖(4〗^2)〗^3= _________________________________________________
d. 〖〖(8〗^4)〗^3/8^10 = __________________________________________________
e. 〖(2^2×3^0)〗^3÷8=______________________________________

Answer 1

\frac{(-5)^{3}.4^{6}.(-5)^{2}}{4.(-5)^{4}}  

= \frac{(-5)^{3+2}.4^{6}}{4.(-5)^{4}}  

= \frac{(-5)^{5}.4^{6}}{4.(-5)^4}  

=(-5)^{5-4}.4^{6-1}

=-5120

\frac{[(-2)^{3}]^{4}.(2^{2})^{3}.[(-3)^{4}]^{3}}{2^{5}.(-2)^{5}.(-3)^{12}}

= \frac{(-2)^{12}.2^{6}.(-3)^{12}}{2^{5}.(-2)^{5}.(-3)^{12}}  

=(-2)^{12-5}.2^{6-5}.(-3)^{12-12}

=(-2)^{7}.2^{1}.(-3)^{0}

=-256

= \frac{(-5)^{6}.3^{4}.(-5).3^{5}}{3^{3}.(-5)^{3}.(-5)^{2}}  

= \frac{(-5)^{7}.3^{7}}{3^{3}.(-5)^{5}}  

=(-5)^{7-5}.3^{7-3}

=(-5)^2.3^{4}

=2025

ponme la mejor respuesta espero ayudarte!!