Solve 35x^3y^3/8p^5q^47xy/64pq/frac{8{p^4{y}^4}{5{x}^2{y}^2}}

$$\frac{ \frac{ 35 { x }^{ 3 } { y }^{ 3 } }{ 8 { p }^{ 5 } { q }^{ 4 } } \frac{ 7xy }{ 64pq } }{ \frac{ 8 { p }^{ 4 } { y }^{ 4 } }{ 5 { x }^{ 2 } { y }^{ 2 } } }$$

Evaluate

$$\frac{1225y^{2}x^{6}}{4096q^{5}p^{10}}$$

Short Solution Steps

Multiply \frac{35x^{3}y^{3}}{8p^{5}q^{4}} times \frac{7xy}{64pq} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{35x^{3}y^{3}\times 7xy}{8p^{5}q^{4}\times 64pq}}{\frac{8p^{4}y^{4}}{5x^{2}y^{2}}}$$

Cancel out y^{2} in both numerator and denominator.

$$\frac{\frac{35x^{3}y^{3}\times 7xy}{8p^{5}q^{4}\times 64pq}}{\frac{8y^{2}p^{4}}{5x^{2}}}$$

Divide \frac{35x^{3}y^{3}\times 7xy}{8p^{5}q^{4}\times 64pq} by \frac{8y^{2}p^{4}}{5x^{2}} by multiplying \frac{35x^{3}y^{3}\times 7xy}{8p^{5}q^{4}\times 64pq} by the reciprocal of \frac{8y^{2}p^{4}}{5x^{2}}.

$$\frac{35x^{3}y^{3}\times 7xy\times 5x^{2}}{8p^{5}q^{4}\times 64pq\times 8y^{2}p^{4}}$$

Cancel out y^{2} in both numerator and denominator.

$$\frac{5\times 7\times 35xyyx^{2}x^{3}}{8\times 8\times 64pqp^{4}q^{4}p^{5}}$$

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

$$\frac{5\times 7\times 35x^{3}yyx^{3}}{8\times 8\times 64pqp^{4}q^{4}p^{5}}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{5\times 7\times 35x^{6}yy}{8\times 8\times 64pqp^{4}q^{4}p^{5}}$$

Multiply y and y to get y^{2}.

$$\frac{5\times 7\times 35x^{6}y^{2}}{8\times 8\times 64pqp^{4}q^{4}p^{5}}$$

Multiply 5 and 7 to get 35.

$$\frac{35\times 35x^{6}y^{2}}{8\times 8\times 64pqp^{4}q^{4}p^{5}}$$

Multiply 35 and 35 to get 1225.

$$\frac{1225x^{6}y^{2}}{8\times 8\times 64pqp^{4}q^{4}p^{5}}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{1225x^{6}y^{2}}{8\times 8\times 64p^{5}qq^{4}p^{5}}$$

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$\frac{1225x^{6}y^{2}}{8\times 8\times 64p^{10}qq^{4}}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{1225x^{6}y^{2}}{8\times 8\times 64p^{10}q^{5}}$$

Multiply 8 and 8 to get 64.

$$\frac{1225x^{6}y^{2}}{64\times 64p^{10}q^{5}}$$

Multiply 64 and 64 to get 4096.

$$\frac{1225x^{6}y^{2}}{4096p^{10}q^{5}}$$

Differentiate w.r.t. x

$$\frac{3675\times \left(\frac{x}{q}\right)^{5}y^{2}}{2048p^{10}}$$