Solve [frac{sqrt{64}+sqrt{4}}{sqrt{144}-sqrt[3]{27}}+2^3/sqrt{81}]^5

$$[ \frac { \sqrt { 64 } + \sqrt { 4 } } { \sqrt { 144 } - \sqrt[ 3 ] { 27 } } + \frac { 2 ^ { 3 } } { \sqrt { 81 } } ] ^ { 5 }$$

Evaluate

$$32$$

Solution Steps

Calculate the square root of 64 and get 8.

$$\left(\frac{8+\sqrt{4}}{\sqrt{144}-\sqrt[3]{27}}+\frac{2^{3}}{\sqrt{81}}\right)^{5}$$

Calculate the square root of 4 and get 2.

$$\left(\frac{8+2}{\sqrt{144}-\sqrt[3]{27}}+\frac{2^{3}}{\sqrt{81}}\right)^{5}$$

Add 8 and 2 to get 10.

$$\left(\frac{10}{\sqrt{144}-\sqrt[3]{27}}+\frac{2^{3}}{\sqrt{81}}\right)^{5}$$

Calculate the square root of 144 and get 12.

$$\left(\frac{10}{12-\sqrt[3]{27}}+\frac{2^{3}}{\sqrt{81}}\right)^{5}$$

Calculate \sqrt[3]{27} and get 3.

$$\left(\frac{10}{12-3}+\frac{2^{3}}{\sqrt{81}}\right)^{5}$$

Subtract 3 from 12 to get 9.

$$\left(\frac{10}{9}+\frac{2^{3}}{\sqrt{81}}\right)^{5}$$

Calculate 2 to the power of 3 and get 8.

$$\left(\frac{10}{9}+\frac{8}{\sqrt{81}}\right)^{5}$$

Calculate the square root of 81 and get 9.

$$\left(\frac{10}{9}+\frac{8}{9}\right)^{5}$$

Add \frac{10}{9} and \frac{8}{9} to get 2.

$$2^{5}$$

Calculate 2 to the power of 5 and get 32.

$$32$$

Factor

$$2^{5}$$