Question

Efectuati : ( 1 supra 5 ) la puterea 0
+ ( 1 supra 5 ) la puterea 17 : [( 1 supra 5 ) la puterea 5 ] la puterea 3.

Answer 1

(1/5)⁰+(1/5)¹⁷:[(1/5)⁵]³

1+(1/5)¹⁷:(1/5)¹⁵

1+(1/5)²

1+1/25

26/25 ✔

Answer 2

Răspuns:

$\frac{26}{25}$

Explicație pas cu pas:

$( \frac{1}{5} )^{0} + {( \frac{1}{5} )}^{17} \div [( \frac{1}{5} )^{5} ]^{3} = \frac{26}{25} \\ 1 + ( \frac{1}{5} )^{17} \div {( \frac{1}{5} )}^{5 \times 3} = \frac{26}{25} \\ 1 + ( \frac{1}{5} ) ^{17} \div {( \frac{1}{5}) }^{15} = \frac{26}{25} \\ 1 + {( \frac{1}{5} })^{17 - 15} = \frac{26}{25} \\ 1 + {( \frac{1}{5}) }^{2} = \frac{26}{25} \\ 1 + \frac{ {1}^{2} }{ {5}^{2} } = \frac{26}{25} \\ 1 + \frac{1}{25} = \frac{26}{25} \\ \frac{25}{25} + \frac{1}{25 } = \frac{25 + 1}{25} = \boxed{ \frac{26}{25} }$

Formule aplicate

${a}^{0} = 1 \: \: \: \: \: a \not = 0 \\ ({a}^{m} ) ^{n} = {a}^{m \times n} \\ {a}^{m} \div {a}^{n} = {a}^{m - n} \\ {( \frac{a}{m}) }^{n} = \frac{ {a}^{n} }{ {m}^{n} }$