Solve (2x^{3}y^{6})(5x^-2y^-4)(4x^-4y^-8)

$$( 2 x ^ { 3 } y ^ { 6 } ) ( 5 x ^ { - 2 } y ^ { - 4 } ) ( 4 x ^ { - 4 } y ^ { - 8 } )$$

Evaluate

$$\frac{40}{x^{3}y^{6}}$$

Solution Steps

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

$$2x^{1}y^{6}\times 5y^{-4}\times 4x^{-4}y^{-8}$$

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

$$2x^{-3}y^{6}\times 5y^{-4}\times 4y^{-8}$$

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

$$2x^{-3}y^{2}\times 5\times 4y^{-8}$$

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

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

Multiply 2 and 5 to get 10.

$$10x^{-3}y^{-6}\times 4$$

Multiply 10 and 4 to get 40.

$$40x^{-3}y^{-6}$$

Differentiate w.r.t. x

$$-\frac{120}{x^{4}y^{6}}$$