Solve (2x^{5}y^{-2})^-2(-2x^-3y^-3)^1

$$( 2 x ^ { 5 } y ^ { - 2 } ) ^ { - 2 } ( - 2 x ^ { - 3 } y ^ { - 3 } ) ^ { 1 }$$

Evaluate

$$-\frac{y}{2x^{13}}$$

Solution Steps

Expand \left(2x^{5}y^{-2}\right)^{-2}.

$$2^{-2}\left(x^{5}\right)^{-2}\left(y^{-2}\right)^{-2}\left(-2x^{-3}y^{-3}\right)^{1}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

$$2^{-2}x^{-10}\left(y^{-2}\right)^{-2}\left(-2x^{-3}y^{-3}\right)^{1}$$

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

$$2^{-2}x^{-10}y^{4}\left(-2x^{-3}y^{-3}\right)^{1}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{1}{4}x^{-10}y^{4}\left(-2x^{-3}y^{-3}\right)^{1}$$

Calculate -2x^{-3}y^{-3} to the power of 1 and get -2x^{-3}y^{-3}.

$$\frac{1}{4}x^{-10}y^{4}\left(-2\right)x^{-3}y^{-3}$$

Multiply \frac{1}{4} and -2 to get -\frac{1}{2}.

$$-\frac{1}{2}x^{-10}y^{4}x^{-3}y^{-3}$$

To multiply powers of the same base, add their exponents. Add -10 and -3 to get -13.

$$-\frac{1}{2}x^{-13}y^{4}y^{-3}$$

To multiply powers of the same base, add their exponents. Add 4 and -3 to get 1.

$$-\frac{1}{2}x^{-13}y^{1}$$

Calculate y to the power of 1 and get y.

$$-\frac{1}{2}x^{-13}y$$

Expand

$$-\frac{y}{2x^{13}}$$

Solution Steps

Expand \left(2x^{5}y^{-2}\right)^{-2}.

$$2^{-2}\left(x^{5}\right)^{-2}\left(y^{-2}\right)^{-2}\left(-2x^{-3}y^{-3}\right)^{1}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

$$2^{-2}x^{-10}\left(y^{-2}\right)^{-2}\left(-2x^{-3}y^{-3}\right)^{1}$$

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

$$2^{-2}x^{-10}y^{4}\left(-2x^{-3}y^{-3}\right)^{1}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{1}{4}x^{-10}y^{4}\left(-2x^{-3}y^{-3}\right)^{1}$$

Calculate -2x^{-3}y^{-3} to the power of 1 and get -2x^{-3}y^{-3}.

$$\frac{1}{4}x^{-10}y^{4}\left(-2\right)x^{-3}y^{-3}$$

Multiply \frac{1}{4} and -2 to get -\frac{1}{2}.

$$-\frac{1}{2}x^{-10}y^{4}x^{-3}y^{-3}$$

To multiply powers of the same base, add their exponents. Add -10 and -3 to get -13.

$$-\frac{1}{2}x^{-13}y^{4}y^{-3}$$

To multiply powers of the same base, add their exponents. Add 4 and -3 to get 1.

$$-\frac{1}{2}x^{-13}y^{1}$$

Calculate y to the power of 1 and get y.

$$-\frac{1}{2}x^{-13}y$$