Solve 7x^-2y^-3*2x^3y^-1*3{x}^4{y}^6

$$7 { x }^{ -2 } { y }^{ -3 } \times 2 { x }^{ 3 } { y }^{ -1 } \times 3 { x }^{ 4 } { y }^{ 6 }$$

Evaluate

$$42y^{2}x^{5}$$

Solution Steps

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

$$7x^{1}y^{-3}\times 2y^{-1}\times 3x^{4}y^{6}$$

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

$$7x^{5}y^{-3}\times 2y^{-1}\times 3y^{6}$$

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

$$7x^{5}y^{-4}\times 2\times 3y^{6}$$

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

$$7x^{5}y^{2}\times 2\times 3$$

Multiply 7 and 2 to get 14.

$$14x^{5}y^{2}\times 3$$

Multiply 14 and 3 to get 42.

$$42x^{5}y^{2}$$

Differentiate w.r.t. x

$$210y^{2}x^{4}$$