Lutasin ang ((-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}

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

I-evaluate

$$\frac{17}{8}=2.125$$

Mga Hakbang ng Solution

Para mag-divide ng mga power na may parehong base, i-subtract ang exponent ng denominator mula sa exponent ng numerator. I-subtract ang 1 sa 3 para makuha ang 2.

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

Para mag-divide ng mga power na may parehong base, i-subtract ang exponent ng denominator mula sa exponent ng numerator. I-subtract ang 3 sa 4 para makuha ang 1.

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

Kalkulahin ang -\frac{1}{4} sa power ng 2 at kunin ang \frac{1}{16}.

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

I-subtract ang \frac{1}{2} mula sa 2 para makuha ang \frac{3}{2}.

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

Kalkulahin ang \frac{3}{2} sa power ng 4 at kunin ang \frac{81}{16}.

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

I-subtract ang \frac{5}{9} mula sa 1 para makuha ang \frac{4}{9}.

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

Kalkulahin ang \frac{4}{9} sa power ng 2 at kunin ang \frac{16}{81}.

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

I-multiply ang \frac{81}{16} at \frac{16}{81} para makuha ang 1.

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

Idagdag ang \frac{1}{16} at 1 para makuha ang \frac{17}{16}.

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

Kalkulahin ang \frac{17}{2} sa power ng 1 at kunin ang \frac{17}{2}.

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

Kalkulahin ang -1 sa power ng 2 at kunin ang 1.

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

I-multiply ang \frac{3}{2} at 1 para makuha ang \frac{3}{2}.

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

Idagdag ang \frac{17}{2} at \frac{3}{2} para makuha ang 10.

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

I-subtract ang 1 mula sa 10 para makuha ang 9.

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

Idagdag ang 9 at \frac{1}{4} para makuha ang \frac{37}{4}.

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

I-divide ang \frac{17}{16} gamit ang \frac{37}{4} sa pamamagitan ng pagmu-multiply sa \frac{17}{16} gamit ang reciprocal ng \frac{37}{4}.

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

I-multiply ang \frac{17}{16} at \frac{4}{37} para makuha ang \frac{17}{148}.

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

I-multiply ang \frac{17}{148} at \frac{37}{2} para makuha ang \frac{17}{8}.

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

I-factor

$$\frac{17}{2 ^ {3}} = 2\frac{1}{8} = 2.125$$