Solve a^{3}b^27ac^414b^2c^3

$$a ^ { 3 } b ^ { 2 } 7 a c ^ { 4 } 14 b ^ { 2 } c ^ { 3 }$$

Evaluate

$$98c^{7}\left(ab\right)^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$a^{4}b^{2}\times 7c^{4}\times 14b^{2}c^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$a^{4}b^{4}\times 7c^{4}\times 14c^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$a^{4}b^{4}\times 7c^{7}\times 14$$

Multiply 7 and 14 to get 98.

$$a^{4}b^{4}\times 98c^{7}$$

Differentiate w.r.t. a

$$392a^{3}b^{4}c^{7}$$