Solve 4x^{4}y^{3}*4x^4y^3*2x^-2y^3

$$4 x ^ { 4 } y ^ { 3 } \cdot 4 x ^ { 4 } y ^ { 3 } \cdot 2 x ^ { - 2 } y ^ { 3 }$$

Evaluate

$$32x^{6}y^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$4x^{8}y^{3}\times 4y^{3}\times 2x^{-2}y^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and -2 to get 6.

$$4x^{6}y^{3}\times 4y^{3}\times 2y^{3}$$

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

$$4x^{6}y^{6}\times 4\times 2y^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$4x^{6}y^{9}\times 4\times 2$$

Multiply 4 and 4 to get 16.

$$16x^{6}y^{9}\times 2$$

Multiply 16 and 2 to get 32.

$$32x^{6}y^{9}$$

Differentiate w.r.t. x

$$192x^{5}y^{9}$$