valor da expressão (4 elevado a 3/2-8 elevado 2/3)elevado a 1/2
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Marina,
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Aplicando propriedades operatórias de potências
![( 4^{ \frac{3}{2} } - 8^{ \frac{2}{3} }) ^{ \frac{1}{2} } \\ \\= [(2^2) ^{ \frac{3}{2} } -(2^3) ^{ \frac{2}{3} } ] ^{ \frac{1}{2} } \\ \\ =( 2^{2. \frac{3}{2} } - 2^{3. \frac{2}{3} } ) ^{ \frac{1}{2} } \\ \\ =(2^3-2^2) ^{ \frac{1}{2} } \\ \\ =(8-4) ^{ \frac{1}{2} } \\ \\ = 4^{ \frac{1}{2} } \\ \\ =(2^2) ^{ \frac{1}{2} } \\ \\ = 2^{2. \frac{1}{2} }](https://tex.z-dn.net/?f=%28+4%5E%7B+%5Cfrac%7B3%7D%7B2%7D+%7D+-+8%5E%7B+%5Cfrac%7B2%7D%7B3%7D+%7D%29+%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+++%5C%5C++%5C%5C%3D+%5B%282%5E2%29+%5E%7B+%5Cfrac%7B3%7D%7B2%7D+%7D+-%282%5E3%29+%5E%7B+%5Cfrac%7B2%7D%7B3%7D+%7D+%5D+%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D++%5C%5C++%5C%5C+%3D%28+2%5E%7B2.+%5Cfrac%7B3%7D%7B2%7D+%7D+-+2%5E%7B3.+%5Cfrac%7B2%7D%7B3%7D+%7D+%29++%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%5C%5C++%5C%5C+%3D%282%5E3-2%5E2%29+%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D++%5C%5C++%5C%5C+%3D%288-4%29+%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D++%5C%5C++%5C%5C+%3D+4%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D++%5C%5C++%5C%5C+%3D%282%5E2%29+%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D++%5C%5C++%5C%5C+%3D+2%5E%7B2.+%5Cfrac%7B1%7D%7B2%7D+%7D+ "( 4^{ \frac{3}{2} } - 8^{ \frac{2}{3} }) ^{ \frac{1}{2} } \\ \\= [(2^2) ^{ \frac{3}{2} } -(2^3) ^{ \frac{2}{3} } ] ^{ \frac{1}{2} } \\ \\ =( 2^{2. \frac{3}{2} } - 2^{3. \frac{2}{3} } ) ^{ \frac{1}{2} } \\ \\ =(2^3-2^2) ^{ \frac{1}{2} } \\ \\ =(8-4) ^{ \frac{1}{2} } \\ \\ = 4^{ \frac{1}{2} } \\ \\ =(2^2) ^{ \frac{1}{2} } \\ \\ = 2^{2. \frac{1}{2} }")
RESULTADO FINAL
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Aplicando propriedades operatórias de potências
marina329:
Obrigada
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