Solve (-3a^2b^2)^2+1/2ab(-3ab)^3

$$( - 3 a ^ { 2 } b ^ { 2 } ) ^ { 2 } + \frac { 1 } { 2 } a b ( - 3 a b ) ^ { 3 }$$

Evaluate

$$-\frac{9\left(ab\right)^{4}}{2}$$

Solution Steps

Expand \left(-3a^{2}b^{2}\right)^{2}.

$$\left(-3\right)^{2}\left(a^{2}\right)^{2}\left(b^{2}\right)^{2}+\frac{1}{2}ab\left(-3ab\right)^{3}$$

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

$$\left(-3\right)^{2}a^{4}\left(b^{2}\right)^{2}+\frac{1}{2}ab\left(-3ab\right)^{3}$$

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

$$\left(-3\right)^{2}a^{4}b^{4}+\frac{1}{2}ab\left(-3ab\right)^{3}$$

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

$$9a^{4}b^{4}+\frac{1}{2}ab\left(-3ab\right)^{3}$$

Expand \left(-3ab\right)^{3}.

$$9a^{4}b^{4}+\frac{1}{2}ab\left(-3\right)^{3}a^{3}b^{3}$$

Calculate -3 to the power of 3 and get -27.

$$9a^{4}b^{4}+\frac{1}{2}ab\left(-27\right)a^{3}b^{3}$$

Multiply \frac{1}{2} and -27 to get -\frac{27}{2}.

$$9a^{4}b^{4}-\frac{27}{2}aba^{3}b^{3}$$

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

$$9a^{4}b^{4}-\frac{27}{2}a^{4}bb^{3}$$

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

$$9a^{4}b^{4}-\frac{27}{2}a^{4}b^{4}$$

Combine 9a^{4}b^{4} and -\frac{27}{2}a^{4}b^{4} to get -\frac{9}{2}a^{4}b^{4}.

$$-\frac{9}{2}a^{4}b^{4}$$

Expand

$$-\frac{9\left(ab\right)^{4}}{2}$$

Solution Steps

Expand \left(-3a^{2}b^{2}\right)^{2}.

$$\left(-3\right)^{2}\left(a^{2}\right)^{2}\left(b^{2}\right)^{2}+\frac{1}{2}ab\left(-3ab\right)^{3}$$

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

$$\left(-3\right)^{2}a^{4}\left(b^{2}\right)^{2}+\frac{1}{2}ab\left(-3ab\right)^{3}$$

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

$$\left(-3\right)^{2}a^{4}b^{4}+\frac{1}{2}ab\left(-3ab\right)^{3}$$

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

$$9a^{4}b^{4}+\frac{1}{2}ab\left(-3ab\right)^{3}$$

Expand \left(-3ab\right)^{3}.

$$9a^{4}b^{4}+\frac{1}{2}ab\left(-3\right)^{3}a^{3}b^{3}$$

Calculate -3 to the power of 3 and get -27.

$$9a^{4}b^{4}+\frac{1}{2}ab\left(-27\right)a^{3}b^{3}$$

Multiply \frac{1}{2} and -27 to get -\frac{27}{2}.

$$9a^{4}b^{4}-\frac{27}{2}aba^{3}b^{3}$$

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

$$9a^{4}b^{4}-\frac{27}{2}a^{4}bb^{3}$$

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

$$9a^{4}b^{4}-\frac{27}{2}a^{4}b^{4}$$

Combine 9a^{4}b^{4} and -\frac{27}{2}a^{4}b^{4} to get -\frac{9}{2}a^{4}b^{4}.

$$-\frac{9}{2}a^{4}b^{4}$$