Solve frac{16y^{5}y^{4}z^3}{14w^-3y^-4z^-5}

$$\frac { 16 y ^ { 5 } y ^ { 4 } z ^ { 3 } } { 14 w ^ { - 3 } y ^ { - 4 } z ^ { - 5 } }$$

Evaluate

$$\frac{8w^{3}z^{8}y^{13}}{7}$$

Solution Steps

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

$$\frac{16y^{9}z^{3}}{14w^{-3}y^{-4}z^{-5}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{8z^{3}y^{9}}{7z^{-5}y^{-4}w^{-3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{8z^{8}y^{13}}{7w^{-3}}$$

Differentiate w.r.t. w

$$\frac{24w^{2}z^{8}y^{13}}{7}$$