Question

alguém me ajude por favor?

Calcule as potências

anexo

Answer 1

a)
           $( \sqrt{2} )^2=( 2^{ \frac{1}{2} } )^2= 2^{ \frac{2}{2} } =2^1=2$

b)
           $( \sqrt[3]{81})^2=81 ^{ \frac{2}{3} }= (27x3) ^{ \frac{2}{3} } = 27^{ \frac{1}{3} } . 3^{ \frac{1}{3} } = \sqrt[3]{27} . \sqrt[3]{3} =3 \sqrt[3]{3}$

c)
           $(4 \sqrt{5} )^3=4^3( 5^{ \frac{1}{2} } )^3=64. 5^{ \frac{3}{2} } =64.5 ^{ \frac{2}{2} } .5 ^{ \frac{1}{2} } =64.5 \sqrt{5} =320 \sqrt{5}$

d)
           $( \sqrt{2}+ \sqrt{3})^2 =( \sqrt{2})^2+2 (\sqrt{2} . \sqrt{3} )+( \sqrt{3})^2=2+2 \sqrt{2x3} +3=5+2 \sqrt{6}$

e)
         $(\sqrt{15})^2= 15$