Matemática, perguntado por Line0, 11 meses atrás

Calcule as expressões usando a propriedade de potenciação ​

Anexos:

Soluções para a tarefa

Respondido por GeBEfte
4

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}}

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