Question

Efectueaza urmatoarele operatii: a) √2⁰ • √2¹ • √2² • ... • √2¹⁰; b) √3⁰ • √3¹ • √3² • ... • √3¹⁰.​

Answer 1

Explicație pas cu pas:

a)

$\sqrt{ {2}^{0} } \cdot \sqrt{ {2}^{1} } \cdot \sqrt{ {2}^{2} }\cdot ...\cdot \sqrt{ {2}^{10} } = \sqrt{{2}^{0} \cdot {2}^{1} \cdot {2}^{2} \cdot ... \cdot {2}^{10}} = \sqrt{ {2}^{0 + 1 + 2 + ... + 10} } = \sqrt{ {2}^{ \frac{10 \cdot 11}{2} } } = \sqrt{ {2}^{55}} = \sqrt{2 \cdot {2}^{54}} = \sqrt{2 \cdot {( {2}^{27} )}^{2}} = {2}^{27} \sqrt{2}$

b)

$\sqrt{ {3}^{0} } \cdot \sqrt{ {3}^{1} } \cdot \sqrt{ {3}^{2} }\cdot ...\cdot \sqrt{ {3}^{10} } = \sqrt{{3}^{0} \cdot {3}^{1} \cdot {3}^{2} \cdot ... \cdot {3}^{10}} = \sqrt{ {3}^{0 + 1 + 2 + ... + 10} } = \sqrt{ {3}^{ \frac{10 \cdot 11}{2} } } = \sqrt{ {3}^{55}} = \sqrt{3 \cdot {3}^{54}} = \sqrt{3 \cdot {( {3}^{27} )}^{2}} = {3}^{27} \sqrt{3}$