Solve {64}^frac{1{6}}{a}^6frac{1{6}}{b}^7frac{1{6}}

$${ 64 }^{ \frac{ 1 }{ 6 } } { a }^{ 6 \frac{ 1 }{ 6 } } { b }^{ 7 \frac{ 1 }{ 6 } }$$

Evaluate

$$2a^{\frac{37}{6}}b^{\frac{43}{6}}$$

Solution Steps

Calculate 64 to the power of \frac{1}{6} and get 2.

$$2a^{\frac{6\times 6+1}{6}}b^{\frac{7\times 6+1}{6}}$$

Multiply 6 and 6 to get 36.

$$2a^{\frac{36+1}{6}}b^{\frac{7\times 6+1}{6}}$$

Add 36 and 1 to get 37.

$$2a^{\frac{37}{6}}b^{\frac{7\times 6+1}{6}}$$

Multiply 7 and 6 to get 42.

$$2a^{\frac{37}{6}}b^{\frac{42+1}{6}}$$

Add 42 and 1 to get 43.

$$2a^{\frac{37}{6}}b^{\frac{43}{6}}$$

Differentiate w.r.t. a

$$\frac{37a^{\frac{31}{6}}b^{\frac{43}{6}}}{3}$$