Solve (a^6b)^6/7

$$( a ^ { 6 } b ) ^ { 6 / 7 }$$

Evaluate

$$b^{\frac{6}{7}}a^{\frac{36}{7}}$$

Solution Steps

Expand \left(a^{6}b\right)^{\frac{6}{7}}.

$$\left(a^{6}\right)^{\frac{6}{7}}b^{\frac{6}{7}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and \frac{6}{7} to get \frac{36}{7}.

$$a^{\frac{36}{7}}b^{\frac{6}{7}}$$

Differentiate w.r.t. a

$$\frac{36b^{\frac{6}{7}}a^{\frac{29}{7}}}{7}$$