Question

10- Reduza a uma potência de mesma base e simplifique:

A) 32.8^4/4^5

B) 81.9^3/27^2

C) 1000^3.10000/100^2

Answer 1

Vamos lá :

a)

$\frac{32 \times {8}^{4} }{ {4}^{5} } = \frac{ {2}^{5} \times ( { {2}^{3}) }^{4} }{( { {2}^{2}) }^{5} } = \frac{ {2}^{5 } \times {2}^{3 \times 4} }{ {2}^{2 \times 5} } = \frac{ {2}^{5} \times {2}^{12} }{ {2}^{10} } = \\ \\ \frac{ {2}^{5 + 12} }{ {2}^{10} } = \frac{ {2}^{17} }{ {2}^{10} } = {2}^{17 - 10} = {2}^{7}$

b)

$\frac{81 \times {9}^{3} }{ {27}^{2} } = \frac{ {3}^{4} \times ( { {3}^{2}) }^{3} }{( { {3}^{3}) }^{2} } = \frac{ {3}^{4} \times {3}^{2 \times 3} }{ {3}^{3 \times 2} } = \frac{ {3}^{4} \times {3}^{6} }{ {3}^{6} } = \\ \\ \frac{ {3}^{4 + 6} }{ {3}^{6} } = \frac{ {3}^{10} }{ {3}^{6} } = {3}^{10 - 6} = {3}^{4}$

c)

$\frac{ {1000}^{3} \times 10000}{ {100}^{2} } = \frac{( { {10}^{3}) }^{3} \times {10}^{4} }{( { {10}^{2}) }^{2} } = \frac{ {10}^{3 \times 3} \times {10}^{4} }{ {10}^{2 \times 2} } = \\ \\ \frac{ {10}^{9} \times {10}^{4} }{ {10}^{4} } = \frac{ {10}^{9 + 4} }{ {10}^{4} } = \frac{ {10}^{13} }{ {10}^{4} } = {10}^{13 - 4} = {10}^{9}$

Espero que tenha ajudado.
Bons estudos.