Solve frac{35x^{3}y^{3}}{8p^{5}q^{4}}*7xy/64pqdiv8p^14q^4/5x^2y^2

$$\frac { 35 x ^ { 3 } y ^ { 3 } } { 8 p ^ { 5 } q ^ { 4 } } \times \frac { 7 x y } { 64 p q } \div \frac { 8 p ^ { 14 } q ^ { 4 } } { 5 x ^ { 2 } y ^ { 2 } }$$

Evaluate

$$\frac{1225\left(xy\right)^{6}}{4096q^{9}p^{20}}$$

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.

$$\frac{\frac{35x^{3}y^{3}\times 7xy}{8p^{5}q^{4}\times 64pq}}{\frac{8p^{14}q^{4}}{5x^{2}y^{2}}}$$

Divide \frac{35x^{3}y^{3}\times 7xy}{8p^{5}q^{4}\times 64pq} by \frac{8p^{14}q^{4}}{5x^{2}y^{2}} by multiplying \frac{35x^{3}y^{3}\times 7xy}{8p^{5}q^{4}\times 64pq} by the reciprocal of \frac{8p^{14}q^{4}}{5x^{2}y^{2}}.

$$\frac{35x^{3}y^{3}\times 7xy\times 5x^{2}y^{2}}{8p^{5}q^{4}\times 64pq\times 8p^{14}q^{4}}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{35x^{4}y^{3}\times 7y\times 5x^{2}y^{2}}{8p^{5}q^{4}\times 64pq\times 8p^{14}q^{4}}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{35x^{6}y^{3}\times 7y\times 5y^{2}}{8p^{5}q^{4}\times 64pq\times 8p^{14}q^{4}}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{35x^{6}y^{4}\times 7\times 5y^{2}}{8p^{5}q^{4}\times 64pq\times 8p^{14}q^{4}}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{35x^{6}y^{6}\times 7\times 5}{8p^{5}q^{4}\times 64pq\times 8p^{14}q^{4}}$$

Multiply 35 and 7 to get 245.

$$\frac{245x^{6}y^{6}\times 5}{8p^{5}q^{4}\times 64pq\times 8p^{14}q^{4}}$$

Multiply 245 and 5 to get 1225.

$$\frac{1225x^{6}y^{6}}{8p^{5}q^{4}\times 64pq\times 8p^{14}q^{4}}$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{1225x^{6}y^{6}}{8p^{6}q^{4}\times 64q\times 8p^{14}q^{4}}$$

To multiply powers of the same base, add their exponents. Add 6 and 14 to get 20.

$$\frac{1225x^{6}y^{6}}{8p^{20}q^{4}\times 64q\times 8q^{4}}$$

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

$$\frac{1225x^{6}y^{6}}{8p^{20}q^{5}\times 64\times 8q^{4}}$$

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

$$\frac{1225x^{6}y^{6}}{8p^{20}q^{9}\times 64\times 8}$$

Multiply 8 and 64 to get 512.

$$\frac{1225x^{6}y^{6}}{512p^{20}q^{9}\times 8}$$

Multiply 512 and 8 to get 4096.

$$\frac{1225x^{6}y^{6}}{4096p^{20}q^{9}}$$

Differentiate w.r.t. x

$$\frac{3675x^{5}y^{6}}{2048q^{9}p^{20}}$$