Solve 7u^{-4}*4x^-1y^9x^-2*2yu^5

$$7 u ^ { - 4 } \cdot 4 x ^ { - 1 } y ^ { 9 } x ^ { - 2 } \cdot 2 y u ^ { 5 }$$

Evaluate

$$\frac{56uy^{10}}{x^{3}}$$

Solution Steps

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

$$7u^{1}\times 4x^{-1}y^{9}x^{-2}\times 2y$$

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

$$7u^{1}\times 4x^{-3}y^{9}\times 2y$$

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$7u^{1}\times 4x^{-3}y^{10}\times 2$$

Calculate u to the power of 1 and get u.

$$7u\times 4x^{-3}y^{10}\times 2$$

Multiply 7 and 4 to get 28.

$$28ux^{-3}y^{10}\times 2$$

Multiply 28 and 2 to get 56.

$$56ux^{-3}y^{10}$$

Differentiate w.r.t. x

$$-\frac{168uy^{10}}{x^{4}}$$