Issolvi left(66^2right)^2sqrt{5/2+3/5(4/6){left(5/5right)}^-2}

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

Evalwa

$$\frac{23328\sqrt{290}}{5}\approx 79452.305028866$$

Passi tas-Soluzzjonijiet

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid 1 u 2 biex tikseb 3.

$$\left(6^{3}\right)^{2}\sqrt{\frac{5}{2}+\frac{3}{5}\times \frac{4}{6}\times \left(\frac{5}{5}\right)^{-2}}$$

Biex tgħolli l-qawwa ta' numru għal qawwa oħra, immultiplika l-esponenti. Immultiplika 3 u 2 biex tikseb 6.

$$6^{6}\sqrt{\frac{5}{2}+\frac{3}{5}\times \frac{4}{6}\times \left(\frac{5}{5}\right)^{-2}}$$

Iddividi 5 b'5 biex tikseb1.

$$6^{6}\sqrt{\frac{5}{2}+\frac{3}{5}\times \frac{4}{6}\times 1^{-2}}$$

Ikkalkula 6 bil-power ta' 6 u tikseb 46656.

$$46656\sqrt{\frac{5}{2}+\frac{3}{5}\times \frac{4}{6}\times 1^{-2}}$$

Naqqas il-frazzjoni \frac{4}{6} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$46656\sqrt{\frac{5}{2}+\frac{3}{5}\times \frac{2}{3}\times 1^{-2}}$$

Immultiplika \frac{3}{5} u \frac{2}{3} biex tikseb \frac{2}{5}.

$$46656\sqrt{\frac{5}{2}+\frac{2}{5}\times 1^{-2}}$$

Ikkalkula 1 bil-power ta' -2 u tikseb 1.

$$46656\sqrt{\frac{5}{2}+\frac{2}{5}\times 1}$$

Immultiplika \frac{2}{5} u 1 biex tikseb \frac{2}{5}.

$$46656\sqrt{\frac{5}{2}+\frac{2}{5}}$$

Żid \frac{5}{2} u \frac{2}{5} biex tikseb \frac{29}{10}.

$$46656\sqrt{\frac{29}{10}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{29}{10}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{29}}{\sqrt{10}}.

$$46656\times \frac{\sqrt{29}}{\sqrt{10}}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{29}}{\sqrt{10}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{10}.

$$46656\times \frac{\sqrt{29}\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

Il-kwadrat ta' \sqrt{10} huwa 10.

$$46656\times \frac{\sqrt{29}\sqrt{10}}{10}$$

Biex timmultiplika \sqrt{29} u \sqrt{10}, immultiplika n-numri taħt l-għerq kwadrat.

$$46656\times \frac{\sqrt{290}}{10}$$

Esprimi 46656\times \frac{\sqrt{290}}{10} bħala frazzjoni waħda.

$$\frac{46656\sqrt{290}}{10}$$

Iddividi 46656\sqrt{290} b'10 biex tikseb\frac{23328}{5}\sqrt{290}.

$$\frac{23328}{5}\sqrt{290}$$