Solve sqrt[4]{5.710^-81/810^20/9.23410^26}

$$\sqrt[ 4 ]{ \frac{ 5.7 { 10 }^{ -8 } \frac{ 1 }{ 8 } { 10 }^{ 20 } }{ 9.234 { 10 }^{ 26 } } }$$

Evaluate

$$\frac{1}{6000}\approx 0.000166667$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -8 and 20 to get 12.

$$\sqrt[4]{\frac{5.7\times 10^{12}\times \frac{1}{8}}{9.234\times 10^{26}}}$$

Cancel out 10^{12} in both numerator and denominator.

$$\sqrt[4]{\frac{\frac{1}{8}\times 5.7}{9.234\times 10^{14}}}$$

Multiply \frac{1}{8} and 5.7 to get \frac{57}{80}.

$$\sqrt[4]{\frac{\frac{57}{80}}{9.234\times 10^{14}}}$$

Calculate 10 to the power of 14 and get 100000000000000.

$$\sqrt[4]{\frac{\frac{57}{80}}{9.234\times 100000000000000}}$$

Multiply 9.234 and 100000000000000 to get 923400000000000.

$$\sqrt[4]{\frac{\frac{57}{80}}{923400000000000}}$$

Express \frac{\frac{57}{80}}{923400000000000} as a single fraction.

$$\sqrt[4]{\frac{57}{80\times 923400000000000}}$$

Multiply 80 and 923400000000000 to get 73872000000000000.

$$\sqrt[4]{\frac{57}{73872000000000000}}$$

Reduce the fraction \frac{57}{73872000000000000} to lowest terms by extracting and canceling out 57.

$$\sqrt[4]{\frac{1}{1296000000000000}}$$

Calculate \sqrt[4]{\frac{1}{1296000000000000}} and get \frac{1}{6000}.

$$\frac{1}{6000}$$

Factor

$$\frac{1}{3 \cdot 2 ^ {4} \cdot 5 ^ {3}} = 0.00016666666666666666$$