Ratkaise [(-2/5)^{2}*(1/4)^{2}]^{2}:(5^{2}*2^{2})^-2-(4/5)^-5*(-4/5)^-4:(frac{4}{5})^-7

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Ratkaisun vaiheet

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Tietokilpailu

Arithmetic

Samanlaisia ongelmia verkkohausta

https://socratic.org/questions/how-do-you-simplify-a-b-a-b-4-4a-2-4b-2-a-b-4-a-2-2ab-b-2-16-16a-4-16b-4

https://socratic.org/questions/how-do-you-find-the-nth-partial-sum-determine-whether-the-series-converges-and-f-9

https://socratic.org/questions/how-to-solve-1-a-2-1-a-3-2-1-a-1-2-a-1-2-1-a-3-2-1-a-1-2-a-1-2-1-a-0-a-1

Jakaa

Kopioitu leikepöydälle

\frac{\left(\frac{4}{25}\times \left(\frac{1}{4}\right)^{2}\right)^{2}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}

Laske -\frac{2}{5} potenssiin 2, jolloin ratkaisuksi tulee \frac{4}{25}.

\frac{\left(\frac{4}{25}\times \frac{1}{16}\right)^{2}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}

Laske \frac{1}{4} potenssiin 2, jolloin ratkaisuksi tulee \frac{1}{16}.

\frac{\left(\frac{1}{100}\right)^{2}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}

Kerro \frac{4}{25} ja \frac{1}{16}, niin saadaan \frac{1}{100}.

\frac{\frac{1}{10000}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}

Laske \frac{1}{100} potenssiin 2, jolloin ratkaisuksi tulee \frac{1}{10000}.

\frac{\frac{1}{10000}}{\left(25\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}

Laske 5 potenssiin 2, jolloin ratkaisuksi tulee 25.

\frac{\frac{1}{10000}}{\left(25\times 4\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}

Laske 2 potenssiin 2, jolloin ratkaisuksi tulee 4.

\frac{\frac{1}{10000}}{100^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}

Kerro 25 ja 4, niin saadaan 100.

\frac{\frac{1}{10000}}{\frac{1}{10000}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}

Laske 100 potenssiin -2, jolloin ratkaisuksi tulee \frac{1}{10000}.

1-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}

Jaa \frac{1}{10000} luvulla \frac{1}{10000}, jolloin ratkaisuksi tulee 1.

1-\left(-\frac{4}{5}\right)^{-4}\times \left(\frac{4}{5}\right)^{2}

Jos haluat jakaa samankantaiset potenssit, vähennä nimittäjän eksponentti osoittajan eksponentista.

1-\frac{625}{256}\times \left(\frac{4}{5}\right)^{2}

Laske -\frac{4}{5} potenssiin -4, jolloin ratkaisuksi tulee \frac{625}{256}.

1-\frac{625}{256}\times \frac{16}{25}