Question

aplicando as propriedades da potência, calcule
Com a resolução por favor ​

Answer 1

a)

$\left[2^3~.~\left(\frac{1}{2}\right)^2\right]^5~=\\\\\\=~\left[2^3~.~\frac{1^2}{2^2}\right]^5~\\\\\\=~\left[\frac{2^3~.~1}{2^2}\right]^5~\\\\\\=~\left[\frac{2^3}{2^2}\right]^5~\\\\\\=~\left[2^{\,3-2}\right]^5~\\\\\\=~\left[2^{1}\right]^5~\\\\\\=~2^{\,1~.~5}~\\\\\\=~2^5~\\\\\\=~\boxed{32}$

b)

$\left(\frac{3}{4}\right)^2~.~\frac{16}{9}~=\\\\\\=~\frac{3^2}{4^2}~.~\frac{16}{9}\\\\\\=~\frac{3^2}{4^2}~.~\frac{4^2}{3^2}\\\\\\=~\frac{3^2~.~4^2}{4^2~.~3^2}\\\\\\=~\frac{1~.~1}{1~.~1}\\\\\\=~\boxed{1}$

c)

$3^0~+~(-3)^2~-~3^2~=\\\\\\=~1~+~9~-~9\\\\\\=~\boxed{1}$