Solve (x^{-2})(x^{3})^2y^-1(y^3)^2

$$( x ^ { - 2 } ) ( x ^ { 3 } ) ^ { 2 } y ^ { - 1 } ( y ^ { 3 } ) ^ { 2 }$$

Evaluate

$$x^{4}y^{5}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$x^{-2}x^{6}y^{-1}\left(y^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$x^{-2}x^{6}y^{-1}y^{6}$$

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

$$x^{4}y^{-1}y^{6}$$

To multiply powers of the same base, add their exponents. Add -1 and 6 to get 5.

$$x^{4}y^{5}$$

Differentiate w.r.t. x

$$4x^{3}y^{5}$$