Question

Qual o resultado das potências?

(3/7)²=
(1/3)-³=
(-5/4)-²=
(-1/2)-³=
​

Answer 1

Potenciação de frações :

--

${ \displaystyle \sf {A) \ \left ( \dfrac{3}{7} \right )^{2} = \large \frac{3^{2} }{7^{2} } = \frac{3\times3}{7\times7} = }} \ \ {\green{{\boxed{{\large \displaystyle \sf {\pink{{ \ \frac{9}{49} \ }}}}}}}}$

${ \displaystyle \sf {B) \ \left ( \dfrac{1}{3} \right )^{-3} = \ \left ( \dfrac{3}{1} \right )^{3} = \ 3^{3} \ = \large 3\times3\times3 = }} \ \ {\green{{\boxed{{\large \displaystyle \sf {\pink{{ \ 27 \ }}}}}}}}$

${ \displaystyle \sf {C) \ \left (- \dfrac{5}{4} \right )^{-2} = \ \left ( -\dfrac{4}{5} \right )^{2} = \large -\frac{4^{2} }{5^{2} } \ = \ - \frac{4\times4}{5\times5} =}} \ \ {\green{{\boxed{{\large \displaystyle \sf {\pink{{ \ -\frac{16}{25} \ }}}}}}}}$

${ \displaystyle \sf {D) \ \left (- \dfrac{1}{2} \right )^{-3} = \ \left (- \dfrac{2}{1} \right )^{3} = \large (-2)^{3} \ = \ (-2)\times(-2)\times(-2) = }} \ \ {\green{{\boxed{{\large \displaystyle \sf {\pink{{ \ -8 \ }}}}}}}}$

____________________________________________

Espero ter ajudado! ❤️