Question

Usando a propriedade das potências de mesmo expoente reduza a uma só potência
A- (-2/3)^3.(5/2)^3
B-(-2)^4.(3)^4.(5)^4
C-(-8)^.(4)^2.(6)^2
D-(-2/3)^3:(5/2)^3
E-(-120)^3:(5)^3
D-(-16)^2:(4)^2

Answer 1

Explicação passo-a-passo:

a)

$( - \frac{2}{3})^{3}.( \frac{5}{2})^{3} = ( - \frac{2}{3}. \frac{5}{2}) ^{3} = ( \frac{5}{3})^{3} = \frac{125}{27}$

b)

$( - 2)^{4}.(3)^{4}.(5)^{4} = ( - 2.3.5)^{4} = ( - 30)^{4} = 810000$

c)

$( - 8)^{2}.(4)^{2}.(6)^{2} = ( - 8.4.6) ^{2} = (192)^{2} = 36864$

d)

$( - \frac{2}{3})^{3} \div ( \frac{5}{2}) ^{3} = ( - \frac{2}{3} \div \frac{5}{2})^{3} = ( - \frac{2}{3}. \frac{2}{5})^{3} = ( - \frac{4}{15}) ^{3} = - \frac{64}{3375}$

e)

$( - 120)^{3} \div (5)^{3} = ( - 120 \div 5)^{3} = ( - {24})^{3} = - 13824$

f)

$( - {16})^{2} \div ( {4})^{2} = ( - 16 \div 4)^{2} = ( - {4})^{2} = 16$