Solve ab^3*(-3a^2b)*5a^3b=

$$a b ^ { 3 } \cdot ( - 3 a ^ { 2 } b ) \cdot 5 a ^ { 3 } b =$$

Evaluate

$$-15b^{5}a^{6}$$

Solution Steps

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

$$a^{3}b^{3}\left(-3\right)b\times 5a^{3}b$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$a^{6}b^{3}\left(-3\right)b\times 5b$$

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

$$a^{6}b^{4}\left(-3\right)\times 5b$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$a^{6}b^{5}\left(-3\right)\times 5$$

Multiply -3 and 5 to get -15.

$$a^{6}b^{5}\left(-15\right)$$

Differentiate w.r.t. a

$$-90\left(ab\right)^{5}$$