Solve sqrt[8]{7/3^-3*7^4}

$$\sqrt[ 8 ]{ \frac{ 7 }{ { 3 }^{ -3 } \times { 7 }^{ 4 } } }$$

Evaluate

$$\frac{343^{\frac{7}{8}}\sqrt[8]{27}}{343}\approx 0.727794393$$

Solution Steps

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\sqrt[8]{\frac{7}{\frac{1}{27}\times 7^{4}}}$$

Calculate 7 to the power of 4 and get 2401.

$$\sqrt[8]{\frac{7}{\frac{1}{27}\times 2401}}$$

Multiply \frac{1}{27} and 2401 to get \frac{2401}{27}.

$$\sqrt[8]{\frac{7}{\frac{2401}{27}}}$$

Divide 7 by \frac{2401}{27} by multiplying 7 by the reciprocal of \frac{2401}{27}.

$$\sqrt[8]{7\times \frac{27}{2401}}$$

Multiply 7 and \frac{27}{2401} to get \frac{27}{343}.

$$\sqrt[8]{\frac{27}{343}}$$