Solve 10a^{5}b^{2}c^3*2a^3b^4c^7=

$$10 a ^ { 5 } b ^ { 2 } c ^ { 3 } \times 2 a ^ { 3 } b ^ { 4 } c ^ { 7 } =$$

Evaluate

$$20b^{6}a^{8}c^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$10a^{8}b^{2}c^{3}\times 2b^{4}c^{7}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$10a^{8}b^{6}c^{3}\times 2c^{7}$$

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$10a^{8}b^{6}c^{10}\times 2$$

Multiply 10 and 2 to get 20.

$$20a^{8}b^{6}c^{10}$$

Differentiate w.r.t. a

$$160b^{6}a^{7}c^{10}$$