Задача 18. Вычислите    \({\left( {{5^{22}}} \right)^4}:{5^{90}}-{\left( {{{343}^7}} \right)^4}:{\left( {{{49}^7}} \right)^6}\)

Ответ

ОТВЕТ: -0,96.

Решение

\({\left( {{5^{22}}} \right)^4}:{5^{90}}-{\left( {{{343}^7}} \right)^4}:{\left( {{{49}^7}} \right)^6} = \dfrac{{{5^{88}}}}{{{5^{90}}}}-\dfrac{{{{\left( {{7^3}} \right)}^{28}}}}{{{{\left( {{7^2}} \right)}^{42}}}} = \)

\( = {5^{88-90}}-\dfrac{{{7^{84}}}}{{{7^{84}}}} = {5^{-2}}-1 = \dfrac{1}{{{5^2}}}-1 = \dfrac{1}{{25}}-1 = -\dfrac{{24}}{{25}} = -0,96.\)

Ответ:  \(-0,96.\)