Solve 15abdiv4b^2*(-6b)

$$15 a b \div 4 b ^ { 2 } \times ( - 6 b )$$

Evaluate

$$-\frac{45ab^{4}}{2}$$

Solution Steps

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

$$\frac{15ab}{4}b^{3}\left(-6\right)$$

Express \frac{15ab}{4}b^{3} as a single fraction.

$$\frac{15abb^{3}}{4}\left(-6\right)$$

Express \frac{15abb^{3}}{4}\left(-6\right) as a single fraction.

$$\frac{-15abb^{3}\times 6}{4}$$

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

$$\frac{-15ab^{4}\times 6}{4}$$

Multiply -15 and 6 to get -90.

$$\frac{-90ab^{4}}{4}$$

Divide -90ab^{4} by 4 to get -\frac{45}{2}ab^{4}.

$$-\frac{45}{2}ab^{4}$$

Differentiate w.r.t. a

$$-\frac{45b^{4}}{2}$$