Solve (64a^6b^7)^1/6

$$( 64 a ^ { 6 } b ^ { 7 } ) ^ { 1 / 6 }$$

Evaluate

$$2\sqrt[6]{a^{6}b^{7}}$$

Solution Steps

Expand \left(64a^{6}b^{7}\right)^{\frac{1}{6}}.

$$64^{\frac{1}{6}}\left(a^{6}\right)^{\frac{1}{6}}\left(b^{7}\right)^{\frac{1}{6}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and \frac{1}{6} to get 1.

$$64^{\frac{1}{6}}a^{1}\left(b^{7}\right)^{\frac{1}{6}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and \frac{1}{6} to get \frac{7}{6}.

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

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

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

Calculate a to the power of 1 and get a.

$$2ab^{\frac{7}{6}}$$

Differentiate w.r.t. a

$$2\times \left(\frac{a}{|a|}\right)^{5}b^{\frac{7}{6}}$$