\left\{0.6\ +\frac{0.387\left(9.283\times{10}^5\right)^{1/6}}{\left[{1+\left(0.559/4.901\right)}^{9/16}\right]^{8/27}}\right\}^2

asked by guest
on Mar 31, 2025 at 1:27 pm



You asked:

Evaluate the expression: (0.6+0.387(9.283⋅105)16(1+0.5594.901)916827)2{\left( 0.6 + \frac{0.387 {\left( 9.283 \cdot {10}^{5} \right)}^{\frac{1}{6}}}{{{\left( 1 + \frac{0.559}{4.901} \right)}^{\frac{9}{16}}}^{\frac{8}{27}}} \right)}^{2}

MathBot Answer:

(0.6+0.387(9.283⋅105)16(1+0.5594.901)916827)2=(35+129⋅174984556⋅21567000)2≈18.9583270540202053627121074353063{\left( 0.6 + \frac{0.387 {\left( 9.283 \cdot {10}^{5} \right)}^{\frac{1}{6}}}{{{\left( 1 + \frac{0.559}{4.901} \right)}^{\frac{9}{16}}}^{\frac{8}{27}}} \right)}^{2} = \left(\frac{3}{5} + \frac{129 \cdot \sqrt[6]{17498455} \cdot 21^{\frac{5}{6}}}{7000}\right)^{2} \approx 18.9583270540202053627121074353063

(0.6+0.387(9.283⋅105)16(1+0.5594.901)916827)2=(610+3871000⋅(9+2831000)⋅1056⋅1((1+5591000⋅14+9011000)916)827)2=(35+3871000⋅(9+2831000)⋅1056⋅1((1+5591000⋅14+9011000)916)827)2=(35+3871000⋅92831000⋅1056⋅1((1+5591000⋅14+9011000)916)827)2=(35+3871000⋅92831000⋅1000006⋅1((1+5591000⋅14+9011000)916)827)2=(35+3871000⋅9283006⋅1((1+5591000⋅14+9011000)916)827)2=(35+3871000⋅103⋅92836⋅1((1+5591000⋅14+9011000)916)827)2=(35+3871000⋅103⋅92836⋅1((1+5591000⋅149011000)916)827)2=(35+3871000⋅103⋅92836⋅1((1+5594901)916)827)2=(35+3871000⋅103⋅92836⋅1((1+43377)916)827)2=(35+3871000⋅103⋅92836⋅1((420377)916)827)2=(35+3871000⋅103⋅92836⋅1(2377⋅28⋅105916⋅377716)827)2=(35+3871000⋅103⋅92836⋅11377⋅23⋅1056⋅37756)2=(35+3871000⋅121⋅2156⋅174984556)2=(35+1297000⋅2156⋅174984556)2\begin{aligned}{\left( 0.6 + \frac{0.387 {\left( 9.283 \cdot {10}^{5} \right)}^{\frac{1}{6}}}{{{\left( 1 + \frac{0.559}{4.901} \right)}^{\frac{9}{16}}}^{\frac{8}{27}}} \right)}^{2}&=\left(\frac{6}{10} + \frac{387}{1000} \cdot \sqrt[6]{\left(9 + \frac{283}{1000}\right) \cdot 10^{5}} \cdot \frac{1}{\left(\left(1 + \frac{559}{1000} \cdot \frac{1}{4 + \frac{901}{1000}}\right)^{\frac{9}{16}}\right)^{\frac{8}{27}}}\right)^{2}\\&=\left(\frac{3}{5} + \frac{387}{1000} \cdot \sqrt[6]{\left(9 + \frac{283}{1000}\right) \cdot 10^{5}} \cdot \frac{1}{\left(\left(1 + \frac{559}{1000} \cdot \frac{1}{4 + \frac{901}{1000}}\right)^{\frac{9}{16}}\right)^{\frac{8}{27}}}\right)^{2}\\&=\left(\frac{3}{5} + \frac{387}{1000} \cdot \sqrt[6]{\frac{9283}{1000} \cdot 10^{5}} \cdot \frac{1}{\left(\left(1 + \frac{559}{1000} \cdot \frac{1}{4 + \frac{901}{1000}}\right)^{\frac{9}{16}}\right)^{\frac{8}{27}}}\right)^{2}\\&=\left(\frac{3}{5} + \frac{387}{1000} \cdot \sqrt[6]{\frac{9283}{1000} \cdot 100000} \cdot \frac{1}{\left(\left(1 + \frac{559}{1000} \cdot \frac{1}{4 + \frac{901}{1000}}\right)^{\frac{9}{16}}\right)^{\frac{8}{27}}}\right)^{2}\\&=\left(\frac{3}{5} + \frac{387}{1000} \cdot \sqrt[6]{928300} \cdot \frac{1}{\left(\left(1 + \frac{559}{1000} \cdot \frac{1}{4 + \frac{901}{1000}}\right)^{\frac{9}{16}}\right)^{\frac{8}{27}}}\right)^{2}\\&=\left(\frac{3}{5} + \frac{387}{1000} \cdot \sqrt[3]{10} \cdot \sqrt[6]{9283} \cdot \frac{1}{\left(\left(1 + \frac{559}{1000} \cdot \frac{1}{4 + \frac{901}{1000}}\right)^{\frac{9}{16}}\right)^{\frac{8}{27}}}\right)^{2}\\&=\left(\frac{3}{5} + \frac{387}{1000} \cdot \sqrt[3]{10} \cdot \sqrt[6]{9283} \cdot \frac{1}{\left(\left(1 + \frac{559}{1000} \cdot \frac{1}{\frac{4901}{1000}}\right)^{\frac{9}{16}}\right)^{\frac{8}{27}}}\right)^{2}\\&=\left(\frac{3}{5} + \frac{387}{1000} \cdot \sqrt[3]{10} \cdot \sqrt[6]{9283} \cdot \frac{1}{\left(\left(1 + \frac{559}{4901}\right)^{\frac{9}{16}}\right)^{\frac{8}{27}}}\right)^{2}\\&=\left(\frac{3}{5} + \frac{387}{1000} \cdot \sqrt[3]{10} \cdot \sqrt[6]{9283} \cdot \frac{1}{\left(\left(1 + \frac{43}{377}\right)^{\frac{9}{16}}\right)^{\frac{8}{27}}}\right)^{2}\\&=\left(\frac{3}{5} + \frac{387}{1000} \cdot \sqrt[3]{10} \cdot \sqrt[6]{9283} \cdot \frac{1}{\left(\left(\frac{420}{377}\right)^{\frac{9}{16}}\right)^{\frac{8}{27}}}\right)^{2}\\&=\left(\frac{3}{5} + \frac{387}{1000} \cdot \sqrt[3]{10} \cdot \sqrt[6]{9283} \cdot \frac{1}{\left(\frac{2}{377} \cdot \sqrt[8]{2} \cdot 105^{\frac{9}{16}} \cdot 377^{\frac{7}{16}}\right)^{\frac{8}{27}}}\right)^{2}\\&=\left(\frac{3}{5} + \frac{387}{1000} \cdot \sqrt[3]{10} \cdot \sqrt[6]{9283} \cdot \frac{1}{\frac{1}{377} \cdot \sqrt[3]{2} \cdot \sqrt[6]{105} \cdot 377^{\frac{5}{6}}}\right)^{2}\\&=\left(\frac{3}{5} + \frac{387}{1000} \cdot \frac{1}{21} \cdot 21^{\frac{5}{6}} \cdot \sqrt[6]{17498455}\right)^{2}\\&=\left(\frac{3}{5} + \frac{129}{7000} \cdot 21^{\frac{5}{6}} \cdot \sqrt[6]{17498455}\right)^{2}\end{aligned}

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