Solve {left(frac{{256}^frac{1{2}}-3*625^0.25}{{128}^frac{1{3}}}right)}^frac{3{7}}

$${ \left( \frac{ { 256 }^{ \frac{ 1 }{ 2 } } -3 \times { 625 }^{ 0.25 } }{ { 128 }^{ \frac{ 1 }{ 3 } } } \right) }^{ \frac{ 3 }{ 7 } }$$

Evaluate

$$0.5$$

Solution Steps

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

$$\left(\frac{16-3\times 625^{0.25}}{128^{\frac{1}{3}}}\right)^{\frac{3}{7}}$$

Calculate 625 to the power of 0.25 and get 5.

$$\left(\frac{16-3\times 5}{128^{\frac{1}{3}}}\right)^{\frac{3}{7}}$$

Multiply 3 and 5 to get 15.

$$\left(\frac{16-15}{128^{\frac{1}{3}}}\right)^{\frac{3}{7}}$$

Subtract 15 from 16 to get 1.

$$\left(\frac{1}{128^{\frac{1}{3}}}\right)^{\frac{3}{7}}$$

To raise \frac{1}{128^{\frac{1}{3}}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{\frac{3}{7}}}{\left(128^{\frac{1}{3}}\right)^{\frac{3}{7}}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{3} and \frac{3}{7} to get \frac{1}{7}.

$$\frac{1^{\frac{3}{7}}}{128^{\frac{1}{7}}}$$

Calculate 1 to the power of \frac{3}{7} and get 1.

$$\frac{1}{128^{\frac{1}{7}}}$$

Calculate 128 to the power of \frac{1}{7} and get 2.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$