Question

O valor da expressão é ?

Answer 1

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$\sf{2^{\frac{1}{4}}\cdot2^{\frac{3}{4}}+3^{\frac{1}{2}}\cdot 3^{\frac{3}{2}}}\\\sf{2^{\frac{1}{4}+\frac{3}{4}}+3^{\frac{1}{2}+\frac{3}{2}}}\\\sf{2^{1}+3^2=2+9=11\checkmark}$

Answer 2

Resposta:

Explicação passo-a-passo:

$\displaystyle\\ 2^{\frac{1}{4} }.2^{\frac{3}{4} }+3^{\frac{1}{2} }.3^{\frac{3}{2} }=\\\\2^{\frac{1}{4}+\frac{3}{4}}+3^{\frac{1}{2}+\frac{3}{2}}=\\\\2^{\frac{1+3}{4} }+3^{\frac{1+3}{2} }=\\\\2^{\frac{4}{4} }+3^{\frac{4}{2} }=\\\\2^{1}+3^{2}=\\\\2+9=\\\\11$

$Propriedades:(a^{m})^{n}=a^{m.n}\\\\\sqrt[n]{x^m} =x^{\frac{m}{n} }\\\\a^{m}a^{n}=a^{m+n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n} \\\\a^{0}=1\\\\a^{1}=a$