Solve (2a^{7}b)(b^2c^5)(5a^-3c^2)

$$( 2 a ^ { 7 } b ) ( b ^ { 2 } c ^ { 5 } ) ( 5 a ^ { - 3 } c ^ { 2 } )$$

Evaluate

$$10b^{3}a^{4}c^{7}$$

Solution Steps

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

$$2a^{4}bb^{2}c^{5}\times 5c^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

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

Multiply 2 and 5 to get 10.

$$10a^{4}b^{3}c^{7}$$

Differentiate w.r.t. a

$$40c^{7}\left(ab\right)^{3}$$