Solve -3a^2b^3*0,5a^3b^4?

$$- 3 a ^ { 2 } b ^ { 3 } \cdot 0,5 a ^ { 3 } b ^ { 4 } ?$$

Evaluate

$$-\frac{3a^{5}b^{7}}{2}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-3\right)^{1}a^{2}b^{3}\times 0,5^{1}a^{3}b^{4}$$

Use the Commutative Property of Multiplication.

$$\left(-3\right)^{1}\times 0,5^{1}a^{2}a^{3}b^{3}b^{4}$$

To multiply powers of the same base, add their exponents.

$$\left(-3\right)^{1}\times 0,5^{1}a^{2+3}b^{3+4}$$

Add the exponents 2 and 3.

$$\left(-3\right)^{1}\times 0,5^{1}a^{5}b^{3+4}$$

Add the exponents 3 and 4.

$$\left(-3\right)^{1}\times 0,5^{1}a^{5}b^{7}$$

Multiply -3 times 0,5.

$$-1,5a^{5}b^{7}$$

Differentiate w.r.t. a

$$-\frac{15a^{4}b^{7}}{2}$$