Kalkulator ułamków
potęgowanie $(8\frac{1}{1})^{147}$

Za pomocą kalkulatora potęgowania ułamków podniesiesz do wybranej potęgi dowolny ułamek zwykły, właściwy, niewłaściwy, dziesiętny lub liczbę mieszaną. Sprawdź jak krok po kroku wykonać obliczenia i wynik potęgowania $(8\frac{1}{1})^{147}$.

Kalkulator potęgowania ułamka $(8\frac{1}{1})^{147}$

Jeżeli musisz podnieść do potęgi inny ułamek to ułamek dziesiętny wpisz w pole liczby całkowitej. Jeśli ułamek jest liczbą mieszaną podaj odpowiednio liczbę całkowitą (może być ujemna) oraz licznik i mianownik ułamka. Jeśli jest to ułamek zwykły lub niewłaściwy, a jego wartość jest ujemna znak minus wstaw przy liczniku. Jeżeli znak minus jest przed nawiasem np. \( -\left(\frac{2}{3}\right)^2 \), wówczas ułamek lub liczbę mieszaną wpisz bez tego znaku, a po otrzymaniu wyniku znak minus dopisz samodzielnie do otrzymanej liczby. Zobacz jak potęgować ułamki bez nawiasów lub z nawiasem

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$$ \boldsymbol{\huge{\style{color:#6059f6;}{\style{font-size:50px;}{(}}\style{color:#6059f6;}{8}\frac{\style{color:#6059f6;}{1}}{\style{color:#6059f6;}{1}}\style{color:#6059f6;}{\style{font-size:50px;}{)}^{147}}= \style{color:#6059f6;}{\frac{1.8777980666473E+140}{1} } = \style{color:#6059f6;}{1.8777980666473E+140} }} $$
Krok 1
Ponieważ pierwsza liczba jest liczbą mieszaną, zamieniamy ją na ułamek niewłaściwy
$$\huge{\style{color:#0b83b3;}{8}\frac{\style{color:#dc4b1d;}{1}}{\style{color:#f7ab45;}{1}} = \frac{\style{color:#0b83b3;}{8} · \style{color:#f7ab45;}{1} + \style{color:#dc4b1d;}{1}}{\style{color:#f7ab45;}{1}} = \style{color:#6059f6;}{\frac{9}{1}} } $$
Licznik ułamka otrzymujemy przez pomnożenie liczby całkowitej 8 razy mianownik 1 plus licznik 1.
Mianownik ułamka niewłaściwego pozostawiamy bez zmian.
Krok 2
Potęgujemy ułamek
Potęgowanie jest to iloczyn takich samych liczb.
Oznacza to, że każdy ułamek musimy przemnożyć przez siebie tyle razy, jaki jest wykładnik potęgi.
Podczas mnożenia ułamków mnożymy przez siebie oddzielnie liczniki i mianowniki.
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Licznik podzielony przez mianownik daje liczbę całkowitą.
$$ \huge{\style{color:#6059f6;}{ \frac{1.8777980666473E+140}{1} = 1.8777980666473E+140} } $$
Podsumowanie
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$$(-\frac{1}{5})^{3}= \style{}{-\frac{1}{125} } $$$$(\frac{13}{15})^{8}= \style{}{\frac{815730721}{2562890625} } $$$$(3\frac{1}{1})^{45}= \style{}{\frac{1.2379400392854E+27}{1} } = \style{}{1.2379400392854E+27} $$$$(\frac{4}{25})^{-2}= \style{}{}\style{}{39} \frac{\style{}{1}}{\style{}{16}}$$$$(\frac{1}{300})^{12}= \style{}{\frac{1}{5.31441E+29} } $$$$(1\frac{2}{5})^{10}= \style{}{}\style{}{28} \frac{\style{}{9037749}}{\style{}{9765625}}$$$$(2\frac{11}{2})^{1} = \style{}{2}\frac{\style{}{11}}{\style{}{2}}$$$$0.75^{-2}= \style{}{}\style{}{1} \frac{\style{}{7}}{\style{}{9}}$$$$(2\frac{50}{65})^{17}= \style{}{}\style{}{33121158} \frac{\style{}{0.87007675692439}}{\style{}{1}}$$$$(35\frac{1}{1})^{-1}= \style{}{\frac{1}{36} } $$$$(\frac{7}{7})^{2}= \style{}{\frac{49}{49} } = \style{}{1} $$$$(\frac{12}{51})^{2}= \style{}{}\style{}{\frac{16}{289}}$$$$(\frac{5}{1})^{-6}= \style{}{\frac{1}{15625} } $$$$(9\frac{1}{27})^{2}= \style{}{}\style{}{81} \frac{\style{}{487}}{\style{}{729}}$$$$(-\frac{1}{2})^{10}= \style{}{\frac{1}{1024} } $$$$(-\frac{3}{1})^{1} = \style{}{-}\frac{\style{}{3}}{\style{}{1}}$$$$0.35^{1} = \style{}{0.35}$$$$(10\frac{5}{8})^{2}= \style{}{}\style{}{112} \frac{\style{}{57}}{\style{}{64}}$$$$(\frac{3}{3})^{6}= \style{}{\frac{729}{729} } = \style{}{1} $$$$(-3\frac{1}{1})^{2}= \style{}{\frac{16}{1} } = \style{}{16} $$$$(\frac{125}{34})^{2}= \style{}{}\style{}{13} \frac{\style{}{597}}{\style{}{1156}}$$$$(1\frac{0.08}{2})^{6}= \style{}{}\style{}{1} \frac{\style{}{1.061276073984}}{\style{}{4}}$$$$(\frac{208}{60})^{2}= \style{}{}\style{}{12} \frac{\style{}{4}}{\style{}{225}}$$$$(\frac{8}{27})^{4}= \style{}{\frac{4096}{531441} } $$$$(\frac{1}{6})^{2}= \style{}{\frac{1}{36} } $$$$(\frac{2}{10})^{-1}= \style{}{\frac{10}{2} } = \style{}{5} $$$$(7\frac{5}{6})^{1} = \style{}{7}\frac{\style{}{5}}{\style{}{6}}$$$$-0.3^{10}= \style{}{\frac{59049}{10000000000} } $$$$(\frac{4}{7})^{-3}= \style{}{}\style{}{5} \frac{\style{}{23}}{\style{}{64}}$$$$(1\frac{15}{100})^{2}= \style{}{}\style{}{1} \frac{\style{}{129}}{\style{}{400}}$$$$(10\frac{0}{1})^{-3}= \style{}{\frac{1}{1000} } $$$$(2\frac{2}{5})^{3}= \style{}{}\style{}{13} \frac{\style{}{103}}{\style{}{125}}$$$$(184\frac{1}{4})^{1} = \style{}{184}\frac{\style{}{1}}{\style{}{4}}$$$$(\frac{5}{8})^{5}= \style{}{\frac{3125}{32768} } $$$$(\frac{8}{1})^{5}= \style{}{\frac{32768}{1} } = \style{}{32768} $$