Solve 4/9x^2y^2*27xdiv3/8xy^2

$$\frac { 4 } { 9 } x ^ { 2 } y ^ { 2 } \times 27 x \div \frac { 3 } { 8 } x y ^ { 2 }$$

Evaluate

$$32\left(xy\right)^{4}$$

Solution Steps

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

$$\frac{\frac{4}{9}x^{3}y^{2}\times 27}{\frac{3}{8}}xy^{2}$$

Multiply \frac{4}{9} and 27 to get 12.

$$\frac{12x^{3}y^{2}}{\frac{3}{8}}xy^{2}$$

Divide 12x^{3}y^{2} by \frac{3}{8} by multiplying 12x^{3}y^{2} by the reciprocal of \frac{3}{8}.

$$\frac{12x^{3}y^{2}\times 8}{3}xy^{2}$$

Multiply 12 and 8 to get 96.

$$\frac{96x^{3}y^{2}}{3}xy^{2}$$

Divide 96x^{3}y^{2} by 3 to get 32x^{3}y^{2}.

$$32x^{3}y^{2}xy^{2}$$

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

$$32x^{4}y^{2}y^{2}$$

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

$$32x^{4}y^{4}$$

Differentiate w.r.t. x

$$128x^{3}y^{4}$$