Solve 5z^{2}*4x^{2}y^4*-3x^3y^3z^-4

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

Evaluate

$$-\frac{60x^{5}y^{7}}{z^{2}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -4 to get -2.

$$5z^{-2}\times 4x^{2}y^{4}\left(-3\right)x^{3}y^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$5z^{-2}\times 4x^{5}y^{4}\left(-3\right)y^{3}$$

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

$$5z^{-2}\times 4x^{5}y^{7}\left(-3\right)$$

Multiply 5 and 4 to get 20.

$$20z^{-2}x^{5}y^{7}\left(-3\right)$$

Multiply 20 and -3 to get -60.

$$-60z^{-2}x^{5}y^{7}$$

Differentiate w.r.t. x

$$-\frac{300x^{4}y^{7}}{z^{2}}$$