Solve 3y^{-9}*3w^-1x^-8y^-7*3x^5w

$$3 y ^ { - 9 } \cdot 3 w ^ { - 1 } x ^ { - 8 } y ^ { - 7 } \cdot 3 x ^ { 5 } w$$

Evaluate

$$\frac{27}{x^{3}y^{16}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -9 and -7 to get -16.

$$3y^{-16}\times 3w^{-1}x^{-8}\times 3x^{5}w$$

Multiply w^{-1} and w to get 1.

$$3y^{-16}\times 3x^{-8}\times 3x^{5}$$

To multiply powers of the same base, add their exponents. Add -8 and 5 to get -3.

$$3y^{-16}\times 3x^{-3}\times 3$$

Multiply 3 and 3 to get 9.

$$9y^{-16}x^{-3}\times 3$$

Multiply 9 and 3 to get 27.

$$27y^{-16}x^{-3}$$

Differentiate w.r.t. x

$$-\frac{81}{x^{4}y^{16}}$$