Question

Simplifique as expressões ​

Answer 1

A)

$\frac{27 \times 243 \times 81}{9 \times 2187} = \frac{3 \times 9 \times 3 \times {9}^{2} \times {9}^{2}}{9 \times 3 \times {9}^{3}} = \\ \\ \frac{ {3}^{2} \times 9 \times{9}^{2} \times{9}^{2} }{3 \times 9 \times {9}^{3} } = \\ \\ \frac{ {3}^{2} \times {9}^{5} }{3 \times {9}^{4} } = {3}^{2 - 1} \times {9}^{5 - 4} = \\ \\ 3 \times 9 = 27$

B)

$\frac{ {7}^{2} \times {49}^{3} \times 343 }{ {7}^{3} \times {7}^{6} } = \frac{ {7}^{2} \times {( {7}^{2})}^{3} \times {7}^{3}}{ {7}^{3} \times {7}^{6} } = \\ \\ \frac{ {7}^{2} \times {7}^{6} \times {7}^{3} }{ {7}^{3} \times {7}^{6} } = \frac{ {7}^{11} }{ {7}^{9} } = {7}^{11 - 9} = {7}^{2} = 49$