Solve 8/5/sqrt{frac{frac{1{3}+5}{3}sqrt[3]{left(2^4-2^3right)^24^3}}}

$$\frac{ \frac{ 8 }{ 5 } }{ \sqrt{ \frac{ \frac{ 1 }{ 3 } +5 }{ 3 } \sqrt[ 3 ]{ { \left( { 2 }^{ 4 } - { 2 }^{ 3 } \right) }^{ 2 } { 4 }^{ 3 } } } }$$

Evaluate

$$\frac{3}{10}=0.3$$

Solution Steps

Add \frac{1}{3} and 5 to get \frac{16}{3}.

$$\frac{\frac{8}{5}}{\sqrt{\frac{\frac{16}{3}}{3}\sqrt[3]{\left(2^{4}-2^{3}\right)^{2}\times 4^{3}}}}$$

Express \frac{\frac{16}{3}}{3} as a single fraction.

$$\frac{\frac{8}{5}}{\sqrt{\frac{16}{3\times 3}\sqrt[3]{\left(2^{4}-2^{3}\right)^{2}\times 4^{3}}}}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{8}{5}}{\sqrt{\frac{16}{9}\sqrt[3]{\left(2^{4}-2^{3}\right)^{2}\times 4^{3}}}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\frac{8}{5}}{\sqrt{\frac{16}{9}\sqrt[3]{\left(16-2^{3}\right)^{2}\times 4^{3}}}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\frac{8}{5}}{\sqrt{\frac{16}{9}\sqrt[3]{\left(16-8\right)^{2}\times 4^{3}}}}$$

Subtract 8 from 16 to get 8.

$$\frac{\frac{8}{5}}{\sqrt{\frac{16}{9}\sqrt[3]{8^{2}\times 4^{3}}}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{\frac{8}{5}}{\sqrt{\frac{16}{9}\sqrt[3]{64\times 4^{3}}}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{\frac{8}{5}}{\sqrt{\frac{16}{9}\sqrt[3]{64\times 64}}}$$

Multiply 64 and 64 to get 4096.

$$\frac{\frac{8}{5}}{\sqrt{\frac{16}{9}\sqrt[3]{4096}}}$$

Calculate \sqrt[3]{4096} and get 16.

$$\frac{\frac{8}{5}}{\sqrt{\frac{16}{9}\times 16}}$$

Multiply \frac{16}{9} and 16 to get \frac{256}{9}.

$$\frac{\frac{8}{5}}{\sqrt{\frac{256}{9}}}$$

Rewrite the square root of the division \frac{256}{9} as the division of square roots \frac{\sqrt{256}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{\frac{8}{5}}{\frac{16}{3}}$$

Divide \frac{8}{5} by \frac{16}{3} by multiplying \frac{8}{5} by the reciprocal of \frac{16}{3}.

$$\frac{8}{5}\times \frac{3}{16}$$

Multiply \frac{8}{5} and \frac{3}{16} to get \frac{3}{10}.

$$\frac{3}{10}$$

Factor

$$\frac{3}{2 \cdot 5} = 0.3$$