Solve (-1/2x^2)(-3x^2y^2)^2

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

Evaluate

$$-\frac{9y^{4}x^{6}}{2}$$

Solution Steps

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

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

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

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

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

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

Calculate -3 to the power of 2 and get 9.

$$-\frac{1}{2}x^{2}\times 9x^{4}y^{4}$$

Multiply -\frac{1}{2} and 9 to get -\frac{9}{2}.

$$-\frac{9}{2}x^{2}x^{4}y^{4}$$

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

$$-\frac{9}{2}x^{6}y^{4}$$

Expand

$$-\frac{9y^{4}x^{6}}{2}$$

Solution Steps

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

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

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

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

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

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

Calculate -3 to the power of 2 and get 9.

$$-\frac{1}{2}x^{2}\times 9x^{4}y^{4}$$

Multiply -\frac{1}{2} and 9 to get -\frac{9}{2}.

$$-\frac{9}{2}x^{2}x^{4}y^{4}$$

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

$$-\frac{9}{2}x^{6}y^{4}$$