Solve frac{7x^{4}y^{3}}{8z^5}div21x^2z^3/4y^5

$$\frac { 7 x ^ { 4 } y ^ { 3 } } { 8 z ^ { 5 } } \div \frac { 21 x ^ { 2 } z ^ { 3 } } { 4 y ^ { 5 } }$$

Evaluate

$$\frac{\left(\frac{y}{z}\right)^{8}x^{2}}{6}$$

Solution Steps

Divide \frac{7x^{4}y^{3}}{8z^{5}} by \frac{21x^{2}z^{3}}{4y^{5}} by multiplying \frac{7x^{4}y^{3}}{8z^{5}} by the reciprocal of \frac{21x^{2}z^{3}}{4y^{5}}.

$$\frac{7x^{4}y^{3}\times 4y^{5}}{8z^{5}\times 21x^{2}z^{3}}$$

Cancel out 4\times 7x^{2} in both numerator and denominator.

$$\frac{x^{2}y^{3}y^{5}}{2\times 3z^{3}z^{5}}$$

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

$$\frac{x^{2}y^{8}}{2\times 3z^{3}z^{5}}$$

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

$$\frac{x^{2}y^{8}}{2\times 3z^{8}}$$

Multiply 2 and 3 to get 6.

$$\frac{x^{2}y^{8}}{6z^{8}}$$

Differentiate w.r.t. x

$$\frac{\left(\frac{y}{z}\right)^{8}x}{3}$$