Question

Sa se calculeze :
c) radical 1 supra 6 la puterea 4 *81 supra 625
d) Radical - 216 supra 343 *1331 supra 8
e) vezi imagininea

Answer 1

$c) \sqrt{ \frac{1}{ {6}^{4} } \times \frac{81}{625} } = \sqrt{ \frac{1}{1296} \times \frac{81}{625} } = \sqrt{ \frac{1 \times 81}{1296 \times 625} } = \sqrt{ \frac{81}{810000} } = \sqrt{ \frac{1}{10000} } = \frac{ \sqrt{1} }{ \sqrt{10000} } = \frac{1}{100}$

$e) \sqrt[14]{ \frac{729 \times {81}^{3} \times {9}^{5} }{ {64}^{2} \times {32}^{3} \times 2 } } = \sqrt[14]{ \frac{ {9}^{3} \times {9}^{6} \times {9}^{5} }{ {2}^{12} \times {2}^{15} \times 2 } } = \sqrt[14]{ \frac{ {9}^{14} }{ {2}^{28} } } = \frac{ \sqrt[14]{ {9}^{14} } }{ \sqrt[14]{ {2}^{28} } } = \frac{9}{ {2}^{2} } = \frac{9}{4}$