Question

hola!com estan espero esten bien. me ayudarian con estos problemaos por favor necesito entregarlo lo mas rapido posible. dare corona y 5 estrellas mas los 75 puntos.
GRACIAAAS!!!

Answer 1

Respuesta:

Explicación:

a.

$15^2\div \:3^2=25\\\\\left(\frac{15}{3}\right)^2=25\\\\5^2=25$

b.

$2^4. \ 5^4=\left[\left(2\right)\left(5\right)\right]^4\\10^4=10.000$

c.

$16^3:8^3\\\\\left(\frac{16}{8}\right)^3=2^3=8$

d.

$12^4:4^4\\\\\left(\frac{12}{4}\right)^4=3^4=81$

e.

$4^3. \ 25^3\\\\\left[\left(4\right)\left(25\right)\right]^3\\100^3=1.000.000$

f.

$\\\\\frac{(8^4. \ 3^4)}{6^4} =\frac{\left[\left(8\right)\left(3\right)\right]^4}{6^4}\\ \\\frac{24^4}{6^4} =(\frac{24}{6})^4=4^4=256$

g.

$\left(2^8:\left(2^2\right)^3\right)^4\\\\(2^8:2^{ 2 . \ 3})^4=(2^8:2^{6})^4=\left(\frac{2^8}{2^6}\right)^4=(2^{8-6})^4=(2^2)^4=2^{(2)(4)}=2^{8}=256$

h.

$\left(\left(2^2\right)^4:\left(2^3\right)^2\right)^3\\\left(\left(2^8\right):\left(2^6\right)\right)^3=(\frac{2^8}{2^6})^3=(2^2)^3= 2^6=64$

i.

$\left[\left(10^3\right)^2\cdot 100^5\right]:1000^4\\\\\\\frac{\left(10^3\right)^2\cdot \:100^5}{1000^4}=\frac{\left(10^3)^2\right\cdot \:(2^2 5^2)^5}{\left(2^3\cdot \:5^3\right)^4}=\frac{\left(10^3)^2\right\cdot \:(2^{2\cdot 5})\cdot( 5^{2\cdot 5})}{\left(2^3\right)^4\left(5^3\right)^4}=\frac{\left(10^3)^2\right\cdot \:(2^{10})\cdot( 5^{10})}{2^{12}\cdot \:5^{12}} =\frac{\left(10^3)^2}{2^{2}\cdot \:5^{2}}=\frac{\left10^6}{2^{2}\cdot \:5^{2}}=\frac{\left(2 \cdot 5)^6}{2^{2}\cdot \:5^{2}}$

$=\frac{2^{6}\cdot \:5^{6}}{2^{2}\cdot \:5^{2}}=2^{4}\cdot \:5^{4}=(2\cdot \:5)^{4}=10^4=10000$