Solve (2a^2b)^2/6asqrt{b}

$$\frac { ( 2 a ^ { 2 } b ) ^ { 2 } } { 6 a \sqrt { b } }$$

Evaluate

$$\frac{2b^{\frac{3}{2}}a^{3}}{3}$$

Short Solution Steps

Expand \left(2a^{2}b\right)^{2}.

$$\frac{2^{2}\left(a^{2}\right)^{2}b^{2}}{6a\sqrt{b}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{2^{2}a^{4}b^{2}}{6a\sqrt{b}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{4}b^{2}}{6a\sqrt{b}}$$

Cancel out 2a in both numerator and denominator.

$$\frac{2b^{2}a^{3}}{3\sqrt{b}}$$

Cancel out \sqrt{b} in both numerator and denominator.

$$\frac{2b^{\frac{3}{2}}a^{3}}{3}$$

Differentiate w.r.t. b

$$\sqrt{b}a^{3}$$