Solve 27^frac{4{3}}+(sqrt{243}4/5)div(sqrt{125})^frac{9{9}}

$$27 ^ { \frac { 4 } { 3 } } + ( \sqrt { 243 } \frac { 4 } { 5 } ) \div ( \sqrt { 125 } ) ^ { \frac { 9 } { 9 } }$$

Evaluate

$$\frac{36\sqrt{15}}{125}+81\approx 82.115419204$$

Short Solution Steps

Divide 9 by 9 to get 1.

$$27^{\frac{4}{3}}+\frac{\sqrt{243}\times \frac{4}{5}}{\left(\sqrt{125}\right)^{1}}$$

Calculate 27 to the power of \frac{4}{3} and get 81.

$$81+\frac{\sqrt{243}\times \frac{4}{5}}{\left(\sqrt{125}\right)^{1}}$$

Factor 243=9^{2}\times 3. Rewrite the square root of the product \sqrt{9^{2}\times 3} as the product of square roots \sqrt{9^{2}}\sqrt{3}. Take the square root of 9^{2}.

$$81+\frac{9\sqrt{3}\times \frac{4}{5}}{\left(\sqrt{125}\right)^{1}}$$

Multiply 9 and \frac{4}{5} to get \frac{36}{5}.

$$81+\frac{\frac{36}{5}\sqrt{3}}{\left(\sqrt{125}\right)^{1}}$$

Calculate \sqrt{125} to the power of 1 and get \sqrt{125}.

$$81+\frac{\frac{36}{5}\sqrt{3}}{\sqrt{125}}$$

Rationalize the denominator of \frac{\frac{36}{5}\sqrt{3}}{\sqrt{125}} by multiplying numerator and denominator by \sqrt{125}.

$$81+\frac{\frac{36}{5}\sqrt{3}\sqrt{125}}{\left(\sqrt{125}\right)^{2}}$$

The square of \sqrt{125} is 125.

$$81+\frac{\frac{36}{5}\sqrt{3}\sqrt{125}}{125}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$81+\frac{\frac{36}{5}\sqrt{3}\times 5\sqrt{5}}{125}$$

Multiply \frac{36}{5} and 5 to get 36.

$$81+\frac{36\sqrt{3}\sqrt{5}}{125}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$81+\frac{36\sqrt{15}}{125}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 81 times \frac{125}{125}.

$$\frac{81\times 125}{125}+\frac{36\sqrt{15}}{125}$$

Since \frac{81\times 125}{125} and \frac{36\sqrt{15}}{125} have the same denominator, add them by adding their numerators.

$$\frac{81\times 125+36\sqrt{15}}{125}$$

Do the multiplications in 81\times 125+36\sqrt{15}.

$$\frac{10125+36\sqrt{15}}{125}$$

Factor

$$\frac{9 {(4 \sqrt{15} + 1125)}}{125} = 82.11541920370775$$