Lutasin ang sqrt{[(1/3+1)^{3}*(2-2/3)^4]^2:[(3/2-1/6)^5*(frac{7}{3}-1)^8]-frac{1}{2}}

$$\sqrt { [ ( \frac { 1 } { 3 } + 1 ) ^ { 3 } \cdot ( 2 - \frac { 2 } { 3 } ) ^ { 4 } ] ^ { 2 } : [ ( \frac { 3 } { 2 } - \frac { 1 } { 6 } ) ^ { 5 } \cdot ( \frac { 7 } { 3 } - 1 ) ^ { 8 } ] - \frac { 1 } { 2 } }$$

I-evaluate

$$\frac{\sqrt{30}}{6}\approx 0.912870929$$

Mga Hakbang ng Solution

Idagdag ang \frac{1}{3} at 1 para makuha ang \frac{4}{3}.

$$\sqrt{\frac{\left(\left(\frac{4}{3}\right)^{3}\left(2-\frac{2}{3}\right)^{4}\right)^{2}}{\left(\frac{3}{2}-\frac{1}{6}\right)^{5}\left(\frac{7}{3}-1\right)^{8}}-\frac{1}{2}}$$

Kalkulahin ang \frac{4}{3} sa power ng 3 at kunin ang \frac{64}{27}.

$$\sqrt{\frac{\left(\frac{64}{27}\left(2-\frac{2}{3}\right)^{4}\right)^{2}}{\left(\frac{3}{2}-\frac{1}{6}\right)^{5}\left(\frac{7}{3}-1\right)^{8}}-\frac{1}{2}}$$

I-subtract ang \frac{2}{3} mula sa 2 para makuha ang \frac{4}{3}.

$$\sqrt{\frac{\left(\frac{64}{27}\times \left(\frac{4}{3}\right)^{4}\right)^{2}}{\left(\frac{3}{2}-\frac{1}{6}\right)^{5}\left(\frac{7}{3}-1\right)^{8}}-\frac{1}{2}}$$

Kalkulahin ang \frac{4}{3} sa power ng 4 at kunin ang \frac{256}{81}.

$$\sqrt{\frac{\left(\frac{64}{27}\times \frac{256}{81}\right)^{2}}{\left(\frac{3}{2}-\frac{1}{6}\right)^{5}\left(\frac{7}{3}-1\right)^{8}}-\frac{1}{2}}$$

I-multiply ang \frac{64}{27} at \frac{256}{81} para makuha ang \frac{16384}{2187}.

$$\sqrt{\frac{\left(\frac{16384}{2187}\right)^{2}}{\left(\frac{3}{2}-\frac{1}{6}\right)^{5}\left(\frac{7}{3}-1\right)^{8}}-\frac{1}{2}}$$

Kalkulahin ang \frac{16384}{2187} sa power ng 2 at kunin ang \frac{268435456}{4782969}.

$$\sqrt{\frac{\frac{268435456}{4782969}}{\left(\frac{3}{2}-\frac{1}{6}\right)^{5}\left(\frac{7}{3}-1\right)^{8}}-\frac{1}{2}}$$

I-subtract ang \frac{1}{6} mula sa \frac{3}{2} para makuha ang \frac{4}{3}.

$$\sqrt{\frac{\frac{268435456}{4782969}}{\left(\frac{4}{3}\right)^{5}\left(\frac{7}{3}-1\right)^{8}}-\frac{1}{2}}$$

Kalkulahin ang \frac{4}{3} sa power ng 5 at kunin ang \frac{1024}{243}.

$$\sqrt{\frac{\frac{268435456}{4782969}}{\frac{1024}{243}\left(\frac{7}{3}-1\right)^{8}}-\frac{1}{2}}$$

I-subtract ang 1 mula sa \frac{7}{3} para makuha ang \frac{4}{3}.

$$\sqrt{\frac{\frac{268435456}{4782969}}{\frac{1024}{243}\times \left(\frac{4}{3}\right)^{8}}-\frac{1}{2}}$$

Kalkulahin ang \frac{4}{3} sa power ng 8 at kunin ang \frac{65536}{6561}.

$$\sqrt{\frac{\frac{268435456}{4782969}}{\frac{1024}{243}\times \frac{65536}{6561}}-\frac{1}{2}}$$

I-multiply ang \frac{1024}{243} at \frac{65536}{6561} para makuha ang \frac{67108864}{1594323}.

$$\sqrt{\frac{\frac{268435456}{4782969}}{\frac{67108864}{1594323}}-\frac{1}{2}}$$

I-divide ang \frac{268435456}{4782969} gamit ang \frac{67108864}{1594323} sa pamamagitan ng pagmu-multiply sa \frac{268435456}{4782969} gamit ang reciprocal ng \frac{67108864}{1594323}.

$$\sqrt{\frac{268435456}{4782969}\times \frac{1594323}{67108864}-\frac{1}{2}}$$

I-multiply ang \frac{268435456}{4782969} at \frac{1594323}{67108864} para makuha ang \frac{4}{3}.

$$\sqrt{\frac{4}{3}-\frac{1}{2}}$$

I-subtract ang \frac{1}{2} mula sa \frac{4}{3} para makuha ang \frac{5}{6}.

$$\sqrt{\frac{5}{6}}$$

I-rewrite ang square root ng division na \sqrt{\frac{5}{6}} bilang division ng mga square root na \frac{\sqrt{5}}{\sqrt{6}}.

$$\frac{\sqrt{5}}{\sqrt{6}}$$

I-rationalize ang denominator ng \frac{\sqrt{5}}{\sqrt{6}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{6}.

$$\frac{\sqrt{5}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

Ang square ng \sqrt{6} ay 6.

$$\frac{\sqrt{5}\sqrt{6}}{6}$$

Para i-multiply ang \sqrt{5} at \sqrt{6}, i-multiply ang mga numero sa ilalim ng square root.

$$\frac{\sqrt{30}}{6}$$