Question

Emplea calculadora y aplicando las propiedades de las potencias, calcula el valor de:
[/tex]$\frac{ 10^{4} }{ 10^{-3} } [tex] \frac{(5 ^{3})^{ \frac{1}{2} } }{5 ^{ \frac{1}{2} } }$ $[(-2) ^{3} ] ^{2}$
$[ \frac{1}{3}] ^{7} * [ \frac{1}{3}] ^{-9}$
$[ \frac{10}{3}] ^{3} : [ \frac{10}{3}] ^{5}$
$3 ^{9}* 5^{3} * 3^{-7} * 5^{-4}$
$( a^{7} a^{-4} )^{2}$
 porfa

Answer 1

Tienes lo siguiente:
1.
$\frac{10^4}{10^{-3}}. \frac{(5^3)^{1/2}}{5^{1/2}}[(-2)^3]^2=(10^{4-(-3)})(5^{3/2-1/2})[-8]^2=\\\\(10^7)(5)(64)=320(10^7)=3,200,000,000$

2.
$(1/3)^7*(1/3)^{-9}=(1/3)^{7-9}=(1/3)^{-2}= \frac{1}{(1/3)^2}= \frac{1}{(1/9)}=9$

3.
$(10/3)^3:(10/3)^5=(10/3)^{3-5}=(10/3)^{-2}=(3/10)^2=9/100=0.09$

4.
$3^9*5^3*3^{-7}*5^{-4}=3^{9-7}*5^{3-4}=3^2*5^{-1}= \frac{3^2}{5}= \frac{9}{5}=1.8$

5.
$(a^7a^{-4})^2=(a^{7-4})^2=(a^3)^2=a^6$

Saludos!