Question

Genteee me ajuda
Sabendo-se que a^2=5^6, b^5 =5^7 e c^3=3^8,calcule (abc)^15, sendo a,b e c números naturais

Answer 1

$\Rightarrow a^2=5^6\\\Rightarrow b^5=5^7\\\Rightarrow c^3=3^8$

$a^2=5^6\\\\\sqrt{a^2}=\sqrt{5^6}\\\\a=5^3\\\\a^{15}=(5^3)^{15}\\\\\boxed{a^{15}=5^{45}}\\\\b^5=5^7\\\\(b^5)^3=(5^7)^3\\\\\boxed{b^{15}=5^{21}}\\\\c^3=3^8\\\\(c^3)^5=(3^8)^5\\\\\boxed{c^{15}=3^{40}}\\\\(abc)^{15}\\\\a^{15}\cdot b^{15}\cdot c^{15}\\\\5^{45}\cdot5^{21}\cdot3^{40}\\\\\boxed{\boxed{3^{40}\cdot5^{66}}}$

Favor, verifique se está correto.

Answer 2

$\sqrt{ a^{2} } = \sqrt{ 5^{6 }$ ∴  a= $5^{6:2} = 5^{3}$

$\sqrt[5]{ b^{5} } = \sqrt[5]{ b^{7} }$ ∴ $b= 5^{ \frac{7}{5} }$
$\sqrt[3]{ c^{3} } = \sqrt[3]{ 3^{8} }$ ∴ $c=3^{ \frac{8}{3} }$

$( 5^{3}* 5^{ \frac{7}{5}}* 3^{ \frac{8}{3} } } } )^{15}$

$( 5^{3*15}* 5^{ \frac{7*15}{5}}* 3^{ \frac{8*15}{3} } } } )$

$5^{45} * 5^{21} * 3^{40}$= $5^{56} * 3^{40}$