Solve sqrt[4]{5.7*10^8*1/8*10^20/9.234*10^26}

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

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 20 to get 28.

$$\sqrt[4]{\frac{5.7\times 10^{28}\times \frac{1}{8}}{9.234\times 10^{26}}}$$

Cancel out 10^{26} in both numerator and denominator.

$$\sqrt[4]{\frac{\frac{1}{8}\times 5.7\times 10^{2}}{9.234}}$$

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

$$\sqrt[4]{\frac{\frac{57}{80}\times 10^{2}}{9.234}}$$

Calculate 10 to the power of 2 and get 100.

$$\sqrt[4]{\frac{\frac{57}{80}\times 100}{9.234}}$$

Multiply \frac{57}{80} and 100 to get \frac{285}{4}.

$$\sqrt[4]{\frac{\frac{285}{4}}{9.234}}$$

Express \frac{\frac{285}{4}}{9.234} as a single fraction.

$$\sqrt[4]{\frac{285}{4\times 9.234}}$$

Multiply 4 and 9.234 to get 36.936.

$$\sqrt[4]{\frac{285}{36.936}}$$

Expand \frac{285}{36.936} by multiplying both numerator and the denominator by 1000.

$$\sqrt[4]{\frac{285000}{36936}}$$

Reduce the fraction \frac{285000}{36936} to lowest terms by extracting and canceling out 456.

$$\sqrt[4]{\frac{625}{81}}$$

Calculate \sqrt[4]{\frac{625}{81}} and get \frac{5}{3}.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$