Solve {left({2}^{2/3}{4}^{1/2}right)}^3{left({2}^frac{1{2}}{4}^frac{5{8}}right)}^4

$${ \left( { 2 }^{ \frac{ 2 }{ 3 } } { 4 }^{ \frac{ 1 }{ 2 } } \right) }^{ 3 } { \left( { 2 }^{ \frac{ 1 }{ 2 } } { 4 }^{ \frac{ 5 }{ 8 } } \right) }^{ 4 }$$

Evaluate

$$4096$$

Solution Steps

Calculate 4 to the power of \frac{1}{2} and get 2.

$$\left(2^{\frac{2}{3}}\times 2\right)^{3}\times \left(2^{\frac{1}{2}}\times 4^{\frac{5}{8}}\right)^{4}$$

To multiply powers of the same base, add their exponents. Add \frac{2}{3} and 1 to get \frac{5}{3}.

$$\left(2^{\frac{5}{3}}\right)^{3}\times \left(2^{\frac{1}{2}}\times 4^{\frac{5}{8}}\right)^{4}$$

Expand \left(2^{\frac{1}{2}}\times 4^{\frac{5}{8}}\right)^{4}.

$$\left(2^{\frac{5}{3}}\right)^{3}\times \left(2^{\frac{1}{2}}\right)^{4}\times \left(4^{\frac{5}{8}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and 4 to get 2.

$$\left(2^{\frac{5}{3}}\right)^{3}\times 2^{2}\times \left(4^{\frac{5}{8}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply \frac{5}{8} and 4 to get \frac{5}{2}.

$$\left(2^{\frac{5}{3}}\right)^{3}\times 2^{2}\times 4^{\frac{5}{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\left(2^{\frac{5}{3}}\right)^{3}\times 4\times 4^{\frac{5}{2}}$$

Calculate 4 to the power of \frac{5}{2} and get 32.

$$\left(2^{\frac{5}{3}}\right)^{3}\times 4\times 32$$

Multiply 4 and 32 to get 128.

$$\left(2^{\frac{5}{3}}\right)^{3}\times 128$$

To raise a power to another power, multiply the exponents. Multiply \frac{5}{3} and 3 to get 5.

$$2^{5}\times 128$$

Calculate 2 to the power of 5 and get 32.

$$32\times 128$$

Multiply 32 and 128 to get 4096.

$$4096$$

Factor

$$2^{12}$$