Solve -16x^4y^5/3*9x^5y^3/8

$$\frac{ -16 { x }^{ 4 } { y }^{ 5 } }{ 3 } \times \frac{ 9 { x }^{ 5 } { y }^{ 3 } }{ 8 }$$

Evaluate

$$-6y^{8}x^{9}$$

Solution Steps

Multiply \frac{-16x^{4}y^{5}}{3} times \frac{9x^{5}y^{3}}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-16x^{4}y^{5}\times 9x^{5}y^{3}}{3\times 8}$$

Cancel out 3\times 8 in both numerator and denominator.

$$-2\times 3y^{3}x^{4}x^{5}y^{5}$$

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

$$-2\times 3y^{8}x^{4}x^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$-2\times 3y^{8}x^{9}$$

Multiply -2 and 3 to get -6.

$$-6y^{8}x^{9}$$

Differentiate w.r.t. x

$$-54\left(xy\right)^{8}$$