Question

Reduza a uma só potência

Answer 1

Vamos utilizar nesta questão as seguintes propriedades de potenciação:

$\rightarrow~~\frac{b^a}{b^c}~=~b^{a-c}\\\\\\\rightarrow~~\left(b^a\right)^c~=~b^{\,a\cdot c}\\\\\\\rightarrow~~\left(\frac{a}{b}\right)^{-c}~=~\left(\frac{b}{a}\right)^{c}$

b)

$\left(-\frac{5}{4}\right)^{-1}:\left(-\frac{5}{4}\right)^{-2}~=\\\\\\=~\left(-\frac{5}{4}\right)^{-1-(-2)}\\\\\\=~\left(-\frac{5}{4}\right)^{-1+2}\\\\\\=~\boxed{\left(-\frac{5}{4}\right)^1}$

c)

$\left[\left(-\frac{3}{2}\right)^2\right]^3~=\\\\\\=~\left(-\frac{3}{2}\right)^{2\,\cdot\,(-3)}\\\\\\=~\boxed{\left(-\frac{3}{2}\right)^{-6}~~~ou~~~\left(-\frac{2}{3}\right)^6}$

d)

$\left[\left(-2,3\right)^0\right]^{-3}~=\\\\\\=~\left(-2,3\right)^{0\,\cdot\,(-3)}\\\\\\=~\boxed{\left(-2,3\right)^{0}}$