Question

escreva na forma de uma unica potencia de3​

Answer 1

Explicação passo-a-passo:

a)

$\sf (3^{\frac{1}{3}})^{\frac{1}{2}}=3^{\frac{1}{3}\cdot\frac{1}{2}}=\red{3^{\frac{1}{6}}}$

b)

$\sf 3^{\frac{2}{3}}\div3^{-\frac{1}{6}}=3^{\frac{2}{3}-\Big(-\frac{1}{6}\Big)}=3^{\frac{2}{3}+\frac{1}{6}}=3^{\frac{4+1}{6}}=\red{3^{\frac{5}{6}}}$

c)

$\sf 27^{\frac{1}{6}}=(3^3)^{\frac{1}{6}}=3^{3\cdot\frac{1}{6}}=3^{\frac{3}{6}}=\red{3^{\frac{1}{2}}}$

Answer 2

Resposta:

a)

(313)12=313⋅12=316\sf (3^{\frac{1}{3}})^{\frac{1}{2}}=3^{\frac{1}{3}\cdot\frac{1}{2}}=\red{3^{\frac{1}{6}}}(3

3

1

)

2

1

=3

3

1

⋅

2

1

=3

6

1

b)

323÷3−16=323−(−16)=323+16=34+16=356\sf 3^{\frac{2}{3}}\div3^{-\frac{1}{6}}=3^{\frac{2}{3}-\Big(-\frac{1}{6}\Big)}=3^{\frac{2}{3}+\frac{1}{6}}=3^{\frac{4+1}{6}}=\red{3^{\frac{5}{6}}}3

3

2

÷3

−

6

1

=3

3

2

−(−

6

1

)

=3

3

2

+

6

1

=3

6

4+1

=3

6

5

c)

2716=(33)16=33⋅16=336=312\sf 27^{\frac{1}{6}}=(3^3)^{\frac{1}{6}}=3^{3\cdot\frac{1}{6}}=3^{\frac{3}{6}}=\red{3^{\frac{1}{2}}}27

6

1

=(3

3

)

6

1

=3

3⋅

6

1

=3

6

3

=3

2

1