Solve (27y^3/8)^2/3

$$( \frac { 27 y ^ { 3 } } { 8 } ) ^ { 2 / 3 }$$

Evaluate

$$\frac{9y^{2}}{4}$$

Solution Steps

To raise \frac{27y^{3}}{8} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(27y^{3}\right)^{\frac{2}{3}}}{8^{\frac{2}{3}}}$$

Expand \left(27y^{3}\right)^{\frac{2}{3}}.

$$\frac{27^{\frac{2}{3}}\left(y^{3}\right)^{\frac{2}{3}}}{8^{\frac{2}{3}}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and \frac{2}{3} to get 2.

$$\frac{27^{\frac{2}{3}}y^{2}}{8^{\frac{2}{3}}}$$

Calculate 27 to the power of \frac{2}{3} and get 9.

$$\frac{9y^{2}}{8^{\frac{2}{3}}}$$

Calculate 8 to the power of \frac{2}{3} and get 4.

$$\frac{9y^{2}}{4}$$

Differentiate w.r.t. y

$$\frac{9y}{2}$$