Solve 256^{frac{2/4}*sqrt[3]{343*(4^{-6}*7^4)^frac{1{2}}}}{64^frac{1{3}}*2401^frac{3{4}}}

$$\frac { 256 ^ { \frac { 2 } { 4 } } \times \sqrt[ 3 ] { 343 \times ( 4 ^ { - 6 } \times 7 ^ { 4 } ) ^ { \frac { 1 } { 2 } } } } { 64 ^ { \frac { 1 } { 3 } } \times 2401 ^ { \frac { 3 } { 4 } } }$$

Evaluate

$$\frac{7^{\frac{2}{3}}}{49}\approx 0.074679708$$

Solution Steps

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{256^{\frac{1}{2}}\sqrt[3]{343\times \left(4^{-6}\times 7^{4}\right)^{\frac{1}{2}}}}{64^{\frac{1}{3}}\times 2401^{\frac{3}{4}}}$$

Calculate 256 to the power of \frac{1}{2} and get 16.

$$\frac{16\sqrt[3]{343\times \left(4^{-6}\times 7^{4}\right)^{\frac{1}{2}}}}{64^{\frac{1}{3}}\times 2401^{\frac{3}{4}}}$$

Calculate 4 to the power of -6 and get \frac{1}{4096}.

$$\frac{16\sqrt[3]{343\times \left(\frac{1}{4096}\times 7^{4}\right)^{\frac{1}{2}}}}{64^{\frac{1}{3}}\times 2401^{\frac{3}{4}}}$$

Calculate 7 to the power of 4 and get 2401.

$$\frac{16\sqrt[3]{343\times \left(\frac{1}{4096}\times 2401\right)^{\frac{1}{2}}}}{64^{\frac{1}{3}}\times 2401^{\frac{3}{4}}}$$

Multiply \frac{1}{4096} and 2401 to get \frac{2401}{4096}.

$$\frac{16\sqrt[3]{343\times \left(\frac{2401}{4096}\right)^{\frac{1}{2}}}}{64^{\frac{1}{3}}\times 2401^{\frac{3}{4}}}$$

Calculate \frac{2401}{4096} to the power of \frac{1}{2} and get \frac{49}{64}.

$$\frac{16\sqrt[3]{343\times \frac{49}{64}}}{64^{\frac{1}{3}}\times 2401^{\frac{3}{4}}}$$

Multiply 343 and \frac{49}{64} to get \frac{16807}{64}.

$$\frac{16\sqrt[3]{\frac{16807}{64}}}{64^{\frac{1}{3}}\times 2401^{\frac{3}{4}}}$$

Calculate 64 to the power of \frac{1}{3} and get 4.

$$\frac{16\sqrt[3]{\frac{16807}{64}}}{4\times 2401^{\frac{3}{4}}}$$

Calculate 2401 to the power of \frac{3}{4} and get 343.

$$\frac{16\sqrt[3]{\frac{16807}{64}}}{4\times 343}$$

Multiply 4 and 343 to get 1372.

$$\frac{16\sqrt[3]{\frac{16807}{64}}}{1372}$$

Divide 16\sqrt[3]{\frac{16807}{64}} by 1372 to get \frac{4}{343}\sqrt[3]{\frac{16807}{64}}.

$$\frac{4}{343}\sqrt[3]{\frac{16807}{64}}$$