Solve 9^{2}*(a^{10})^{2}*(b^6)^2*(c^4)^2

$$9 ^ { 2 } \times ( a ^ { 10 } ) ^ { 2 } \times ( b ^ { 6 } ) ^ { 2 } \times ( c ^ { 4 } ) ^ { 2 }$$

Evaluate

$$81c^{8}b^{12}a^{20}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 10 and 2 to get 20.

$$9^{2}a^{20}\left(b^{6}\right)^{2}\left(c^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$9^{2}a^{20}b^{12}\left(c^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$9^{2}a^{20}b^{12}c^{8}$$

Calculate 9 to the power of 2 and get 81.

$$81a^{20}b^{12}c^{8}$$

Differentiate w.r.t. a

$$1620c^{8}b^{12}a^{19}$$