Question

Calcule as expressões usando a propriedade de potenciação ​

Answer 1

a)

$5^4~.~5^{-2}~~=~~5^{4+(-2)}~~=~~5^{2}~~=~~\boxed{25}$

b)

$\frac{\left(\frac{1}{3}\right)^{-3}}{\left(\frac{1}{3}\right)^2}~~=~~\left(\frac{1}{3}\right)^{-3-2}~~=~~\left(\frac{1}{3}\right)^{-5}~~=~~(3)^5~~=~~\boxed{243}$

c)

$\frac{7^5}{7^{-3}}~~=~~7^{\,5-(-3)}~~=~~7^{\,5+3}~~=~~7^{8}~~=~~\boxed{5764801}$

d)

$\frac{5^{-1}}{5^{-2}}~~=~~5^{-1-(-2)}~=~5^{-1+2}~~=~~5^1~~=~~\boxed{5}$

e)

$\left(6^{-3}\right)^{-2}~~=~~6^{-3~.~(-2)}~~=~~6^{6}~~=~~\boxed{46656}$

f)

$\frac{3^{-6}}{3}~~=~~\frac{3^{-6}}{3^1}~~=~~3^{-6-1}~~=~~3^{-7}~~=~~\left(\frac{1}{3}\right)^7~~=~~\frac{1^7}{3^7}~~=~~\boxed{\frac{1}{2187}}$