Propriedades das potências com expoentes inteiros Resolva Com Cálculos A) (11.²13⁴)³ (11.³13⁵)² B).... Pergunta de ideia deAnaj5

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Algumas propriedades da fração :

Potência de potência de bases iguais se multiplica os expoentes ...

Multiplicação se soma os expoentes ...

Divisão se subtrai os expoentes ...

Vamos la !

$a)\ \frac{(11^{2}.13^{4})^{3}}{(11^{3}.13^{5})^{2}} \\\\\\\\= \frac{11^{2.3}.13^{4.3}}{11^{3.2}.13^{5.2}} \\\\\\\\= \frac{11^{6}.13^{12}}{11^{6}.13^{10}} \\\\\\\\= 13^{12-10} \\\\\\\\= \boxed{13^{2}}$

$b)\ \frac{(2^{-4})^{2}.(5^{-2})^{-3}}{2^{-3}.2^{-11}} \\\\\\\\= \frac{2^{-4.2}.5^{-2.-3}}{2^{-3-11}} \\\\\\\\ = \frac{2^{-8}.5^{-6}}{2^{-14}} \\\\\\\\=2^{-8-(-14)}.5^{6}\\\\\\\\=2^{-8+14}.5^{6}\\\\\\\\=\boxed{2^{6}.5^{6}}$

$c)\ \frac{343^{4}}{7^{11}} \\\\\\\\= \frac{7^{3.4}}{7^{11}} \\\\\\\\= \frac{7^{12}}{7^{11}} \\\\\\\\=7^{12-11}\\\\\\\\=\boxed{7^{1}}$

$d)\ \frac{(4^{2})^{4}.4^{-5}}{2^{10}.2^{-2}} \\\\\\\\= \frac{4^{2.4}.4^{-5}}{2^{10-2}} \\\\\\\\=\frac{4^{8}.4^{-5}}{2^{8}}\\\\\\\\= \frac{4^{8-5}}{2^{2.4}} \\\\\\\\= \frac{4^{3}}{4^{4}} \\\\\\\\=4^{3-4}\\\\\\\\=\boxed{4^{-1}}\ \ \ \ \ \ \ \ ok$

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Anaj5 okay

Anaj5 Obrigadaa

PauloBarros A) 2.3 4.3
(11².13⁴)³ = 11 . 13
----------------- ----------------------------------
(11³.13⁵)² 3.2 5.2
11 . 13

= 11^6.13^12
-------------------
11^6.13^10

12 - 10 2
= 13 = 13

*****************************
b)
   3
[ - 2 ]
= (2⁴)².[5   ]
------------------------
2³.2¹¹

8 - 6    8 - 6
= 2 . 5 = 2 . 5
--------------- ---------------------
3 + 11 14
2 2

8 - 14 - 6
= 2    .5

- 6 - 6
= 2 .5

****************************************
c)
= 343⁴/7¹¹

= (7³)⁴
------------
7¹¹

= 7^12
--------
7^11

12 - 11
= 7

= 7¹

= 7

**********************************
d)
= (4²)⁴.4⁵
---------------------
   2¹⁰.2²

= 4⁸.4⁵
---------------
(10+2)
2

8 + 5
= 4
------------
2^12

= 4^13
----------
2^12

13
= (2²)
--------------
  12
2

26
= 2
--------
12
2

(26 - 12)
= 2

14
= 2

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