Rešite ((-1/4)^{3}:(-1/4)+(2-1/2)^{4}(1-5/9)^2):[(frac{17}{2})^4:(frac{17}{2})^3+frac{3}{2}*(-1)^2-1+frac{1}{4}]*frac{37}{2}

$$( ( - \frac { 1 } { 4 } ) ^ { 3 } : ( - \frac { 1 } { 4 } ) + ( 2 - \frac { 1 } { 2 } ) ^ { 4 } ( 1 - \frac { 5 } { 9 } ) ^ { 2 } ) : [ ( \frac { 17 } { 2 } ) ^ { 4 } : ( \frac { 17 } { 2 } ) ^ { 3 } + \frac { 3 } { 2 } \cdot ( - 1 ) ^ { 2 } - 1 + \frac { 1 } { 4 } ] \cdot \frac { 37 } { 2 }$$

Ovrednoti

$$\frac{17}{8}=2,125$$

Koraki rešitve

Če želite deliti potence enake osnove, odštejte eksponent imenovalca od eksponenta števca. Odštejte 1 od 3, da dobite 2.

$$\frac{\left(-\frac{1}{4}\right)^{2}+\left(2-\frac{1}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\frac{\left(\frac{17}{2}\right)^{4}}{\left(\frac{17}{2}\right)^{3}}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Če želite deliti potence enake osnove, odštejte eksponent imenovalca od eksponenta števca. Odštejte 3 od 4, da dobite 1.

$$\frac{\left(-\frac{1}{4}\right)^{2}+\left(2-\frac{1}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Izračunajte potenco -\frac{1}{4} števila 2, da dobite \frac{1}{16}.

$$\frac{\frac{1}{16}+\left(2-\frac{1}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Odštejte \frac{1}{2} od 2, da dobite \frac{3}{2}.

$$\frac{\frac{1}{16}+\left(\frac{3}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Izračunajte potenco \frac{3}{2} števila 4, da dobite \frac{81}{16}.

$$\frac{\frac{1}{16}+\frac{81}{16}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Odštejte \frac{5}{9} od 1, da dobite \frac{4}{9}.

$$\frac{\frac{1}{16}+\frac{81}{16}\times \left(\frac{4}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Izračunajte potenco \frac{4}{9} števila 2, da dobite \frac{16}{81}.

$$\frac{\frac{1}{16}+\frac{81}{16}\times \frac{16}{81}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Pomnožite \frac{81}{16} in \frac{16}{81}, da dobite 1.

$$\frac{\frac{1}{16}+1}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Seštejte \frac{1}{16} in 1, da dobite \frac{17}{16}.

$$\frac{\frac{17}{16}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Izračunajte potenco \frac{17}{2} števila 1, da dobite \frac{17}{2}.

$$\frac{\frac{17}{16}}{\frac{17}{2}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Izračunajte potenco -1 števila 2, da dobite 1.

$$\frac{\frac{17}{16}}{\frac{17}{2}+\frac{3}{2}\times 1-1+\frac{1}{4}}\times \frac{37}{2}$$

Pomnožite \frac{3}{2} in 1, da dobite \frac{3}{2}.

$$\frac{\frac{17}{16}}{\frac{17}{2}+\frac{3}{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Seštejte \frac{17}{2} in \frac{3}{2}, da dobite 10.

$$\frac{\frac{17}{16}}{10-1+\frac{1}{4}}\times \frac{37}{2}$$

Odštejte 1 od 10, da dobite 9.

$$\frac{\frac{17}{16}}{9+\frac{1}{4}}\times \frac{37}{2}$$

Seštejte 9 in \frac{1}{4}, da dobite \frac{37}{4}.

$$\frac{\frac{17}{16}}{\frac{37}{4}}\times \frac{37}{2}$$

Delite \frac{17}{16} s/z \frac{37}{4} tako, da pomnožite \frac{17}{16} z obratno vrednostjo \frac{37}{4}.

$$\frac{17}{16}\times \frac{4}{37}\times \frac{37}{2}$$

Pomnožite \frac{17}{16} in \frac{4}{37}, da dobite \frac{17}{148}.

$$\frac{17}{148}\times \frac{37}{2}$$

Pomnožite \frac{17}{148} in \frac{37}{2}, da dobite \frac{17}{8}.

$$\frac{17}{8}$$

Faktoriziraj

$$\frac{17}{2 ^ {3}} = 2\frac{1}{8} = 2,125$$