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

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

Evaluate

$$-\frac{6y^{3}}{x^{9}}$$

Solution Steps

Expand \left(x^{-3}y^{2}\right)^{4}.

$$\left(x^{-3}\right)^{4}\left(y^{2}\right)^{4}\left(-6\right)x^{3}y^{-5}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 4 to get -12.

$$x^{-12}\left(y^{2}\right)^{4}\left(-6\right)x^{3}y^{-5}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$x^{-12}y^{8}\left(-6\right)x^{3}y^{-5}$$

To multiply powers of the same base, add their exponents. Add -12 and 3 to get -9.

$$x^{-9}y^{8}\left(-6\right)y^{-5}$$

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

$$x^{-9}y^{3}\left(-6\right)$$

Expand

$$-\frac{6y^{3}}{x^{9}}$$

Solution Steps

Expand \left(x^{-3}y^{2}\right)^{4}.

$$\left(x^{-3}\right)^{4}\left(y^{2}\right)^{4}\left(-6\right)x^{3}y^{-5}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 4 to get -12.

$$x^{-12}\left(y^{2}\right)^{4}\left(-6\right)x^{3}y^{-5}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$x^{-12}y^{8}\left(-6\right)x^{3}y^{-5}$$

To multiply powers of the same base, add their exponents. Add -12 and 3 to get -9.

$$x^{-9}y^{8}\left(-6\right)y^{-5}$$

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

$$x^{-9}y^{3}\left(-6\right)$$