Question

Resolva as expressões:

(8.6)^2/8^8.6^4 =

(2^3.5^4)^4/(2^3.5^10) =

(5.3)^12/5^9. (3^3)^3

Answer 1

$\frac{(8.6)^2}{8^8.6^4} =\frac{8^2.6^2}{8^8.6^4} = 8^{2-8}.6^{2-4} =8^{-6}.6^{-2} = \frac{1}{262144.36} = \frac{1}{9437184}$

$= \frac{(2^3.5^4)^4}{(2^3.5^{10})} = \frac{2^{12}.5^{16}}{(2^3.5^{10})} = 2^{12-3}.5^{16-10} = 2^{9}.5^{6} = 512 . 15625 = 8000000$

$\frac{(5.3)^{12}}{5^9. (3^3)^3} =\frac{5^{12}.3^{12}}{5^9. 3^{9}} = 5^{12-9}.3^{12-9}=5^{3}.3^{3} = (5.3)^{3}=15^{3} = 3375$

Answer 2

$\boxed{\frac{(8.6)^2}{8^8.6^4} =\frac{8^2.6^2}{8^8.6^4}=\frac{1}{8^6.6^2}=\frac{1}{9437184}}$

$\boxed{\frac{(2^3.5^4)^4}{2^3.5^{10}} =\frac{2^{12}.5^{16}}{2^3.5^{10}}=2^9.5^6=8.000.000}$

$\boxed{\frac{(5.3)^{12}}{5^9. (3^3)^3}=\frac{5^{12}.3^{12}}{5^9.3^9}=5^3.3^3=15^3=3375}$