Question

qual e resposta ³√√10³x100³?

Answer 1

$\sqrt[3]{ \sqrt{ {10}^{3} \times {100}^{3} } } = \sqrt[3]{ \sqrt{ {10}^{3} \times { ({10}^{2} )}^{3} } } \\ = \sqrt[3]{ \sqrt{ {10}^{3} \times {10}^{6} } } = \sqrt[3]{ \sqrt{ {10}^{9} } } \\ = \sqrt[3]{ {10}^{ \frac{9}{2} } } = {( {10}^{ \frac{9}{2} } )}^{ \frac{1}{3} } = {10}^{ \frac{9}{2} \times \frac{1}{3} } = {10}^{ \frac{3}{2} } \\ = \sqrt{ {10}^{3} } = 10 \sqrt{10} \\ \boxed{ \textrm{Resposta: }\: 10 \sqrt{10} }$