Página — Matematica 8 (pág. 38)

Aprende

• Al dividir potencias de igual base, se conserva la base y se restan los exponentes.

a^{n}:a^{m}=\frac{a^{n}}{a^{m}}=\frac{\overbrace{(a\cdot a\cdot a\cdot\cdots\cdot a)}^{n\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}\cdot f_{a}}\cdot f_{a}\cdot f_{a}\cdot f_{a}}\cdot f_{a}\cdot f_{a}}\cdot f_{a}\cdot f_{a}\cdot f_{a}}\cdot f_{a^{a}}_{a_{a}}\cdot f_{a}}_{a^{a}}_{a^{a}}_{a^{a}}_{a^{a}}_{a^{a}}_{a^{a}}_{a^{a}}_{a^{a}_{a}}_{a^{a}}_{a^{a}}_{a^{a}}_{a^{a}}_{a^{a}}_{a^{a}}}_{a^{a^{a}}}_{a^{a^{a}}}_{a^{a^{a}}}_{a^{a^{a}}}_{a^{a^{a}}}_{a^{a^{a}}}_{a^{a^{}}}}_{a^{a^{a^{}}}}_{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{}}}}}}}}_{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac

Ejemplo:7^{4}:7^{2}=7^{4-2}=7^{2}

Ejemplo 4

Representa como una potencia el resultado de.(4^{5}:4^{2}):2^{3}

\begin{aligned}\left(4^{5}:4^{2}\right):2^{3}=&\left(\frac{4^{5}}{4^{2}}\right):2^{3}\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\\=&\left(\frac{4\cdot4\cdot4\cdot4\cdot4}{4\cdot4}\right):2^{3}\\=&\frac{4^{3}}{2^{3}}\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\\=&(4:2)^{3}\\=&2^{3}\end{aligned} Escribes como fracción y aplicas la definición de potencias de igual base as.

Ejemplo 6

Un tipo de bacteria se duplica cada 6 min. jCuántas bacterias habia en un comienzo si luego de una hora hay 2 048 bacterias?

Plantea la expresión que representa el problema.

Como las bacterias se duplican cada 6 min, en una hora hay 10 intervalos de tiempo de 6 min.

Cantidad de bacterias que había en un comienzo.

\textcircled{x}\cdot2\textcircled{0}=2048

Expresa el número 2 048 como una potencia de base 2 y resuelve.

\begin{aligned}x\cdot2^{10}=2048\Leftrightarrow&x\cdot2^{10}=2^{11}\\&x=2^{11}:2^{10}\\&x=2^{11-10}\\&x=2\end{aligned}

Entonces, en un comienzo habia 2 bacterias.

Herramientastecnológicas

Para practicar la multiplicación y división de potencias, puedes utilizar el siguiente recurso:https://www.geogebra.org/m/pagKgma9#material/tvWNZpuS

Intervalos de tiempo de 10 minutos	1	2	3	4	5	6
Cantidad de bacterias	2	22	23	24	25	26


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Unidad 1 ·Números