Solve frac{(a^4)^frac{1{3}}}{9}+a/81^3/4

$$\frac { ( a ^ { 4 } ) ^ { \frac { 1 } { 3 } } } { 9 } + \frac { a } { 81 ^ { 3 / 4 } }$$

Factor

$$\frac{\left(3\sqrt[3]{a}+1\right)a}{27}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and \frac{1}{3} to get \frac{4}{3}.

$$factor(\frac{a^{\frac{4}{3}}}{9}+\frac{a}{81^{\frac{3}{4}}})$$

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

$$factor(\frac{a^{\frac{4}{3}}}{9}+\frac{a}{27})$$

Factor out \frac{1}{27}.

$$\frac{3a^{\frac{4}{3}}+a}{27}$$

Consider 3a^{\frac{4}{3}}+a. Factor out a.

$$a\left(3\sqrt[3]{a}+1\right)$$

Rewrite the complete factored expression.

$$\frac{a\left(3\sqrt[3]{a}+1\right)}{27}$$

Evaluate

$$\frac{a^{\frac{4}{3}}}{9}+\frac{a}{27}$$