Solve 6x^{4}*3x^-9y^-3y^-4*3y^-1

$$6 x ^ { 4 } \cdot 3 x ^ { - 9 } y ^ { - 3 } y ^ { - 4 } \cdot 3 y ^ { - 1 }$$

Evaluate

$$\frac{54}{x^{5}y^{8}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and -9 to get -5.

$$6x^{-5}\times 3y^{-3}y^{-4}\times 3y^{-1}$$

To multiply powers of the same base, add their exponents. Add -3 and -4 to get -7.

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

To multiply powers of the same base, add their exponents. Add -7 and -1 to get -8.

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

Multiply 6 and 3 to get 18.

$$18x^{-5}y^{-8}\times 3$$

Multiply 18 and 3 to get 54.

$$54x^{-5}y^{-8}$$

Differentiate w.r.t. x

$$-\frac{270}{x^{6}y^{8}}$$