Question

Aplique as propriedades das potências e reduza a uma só potência. fracões por favor me ajude ta muito dificil pra mim essa merd*. a) (5/13)^10 : (5/13)^-6= b) (1/2)^4 . (1/2)^3 . [(1/2)^4]^3 c) (4/5)^4 . (4/5)^6= d) [(−0,5)^6]^−1

Answer 1

Resposta:

Explicação passo-a-passo:

a) $(5/13)^{10} : (5/13)^{-6}= \frac{(\frac{5}{13})^{10}}{(\frac{5}{13})^{-6}} =(\frac{5}{13})^{10-(-6)}=(\frac{5}{13})^{10+6}=(\frac{5}{13})^{16}$

b) $(1/2)^4 . (1/2)^3 . [(1/2)^4]^3 =$ $(\frac{1}{2})^{4}.(\frac{1}{2})^{3}.((\frac{1}{2})^{4})^{3}=(\frac{1}{2})^{4}.(\frac{1}{2})^{3}.(\frac{1}{2})^{4.3}=(\frac{1}{2})^{4}.(\frac{1}{2})^{3}.(\frac{1}{2})^{12}=(\frac{1}{2})^{4+3+12}=(\frac{1}{2})^{19}$

c) $(4/5)^4 . (4/5)^6=(\frac{4}{5})^{4}.(\frac{4}{5})^{6}=(\frac{4}{5})^{4+6}=(\frac{4}{5})^{10}$

d) $[(-0,5)^6]^{-1}=(-0,5)^{6.(-1)}=(-0,5)^{-6}=(-\frac{5}{10} )^{-6}=(-\frac{10}{5} )^{6}=(-2 )^{6}=64$