Solve 3(-2a^3)^2*2(-3a^2)^3

$$3 ( - 2 a ^ { 3 } ) ^ { 2 } \times 2 ( - 3 a ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-648a^{12}$$

Solution Steps

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

$$3\left(-2\right)^{2}\left(a^{3}\right)^{2}\times 2\left(-3a^{2}\right)^{3}$$

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

$$3\left(-2\right)^{2}a^{6}\times 2\left(-3a^{2}\right)^{3}$$

Calculate -2 to the power of 2 and get 4.

$$3\times 4a^{6}\times 2\left(-3a^{2}\right)^{3}$$

Multiply 3 and 4 to get 12.

$$12a^{6}\times 2\left(-3a^{2}\right)^{3}$$

Multiply 12 and 2 to get 24.

$$24a^{6}\left(-3a^{2}\right)^{3}$$

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

$$24a^{6}\left(-3\right)^{3}\left(a^{2}\right)^{3}$$

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

$$24a^{6}\left(-3\right)^{3}a^{6}$$

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

$$24a^{6}\left(-27\right)a^{6}$$

Multiply 24 and -27 to get -648.

$$-648a^{6}a^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$-648a^{12}$$

Expand

$$-648a^{12}$$

Solution Steps

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

$$3\left(-2\right)^{2}\left(a^{3}\right)^{2}\times 2\left(-3a^{2}\right)^{3}$$

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

$$3\left(-2\right)^{2}a^{6}\times 2\left(-3a^{2}\right)^{3}$$

Calculate -2 to the power of 2 and get 4.

$$3\times 4a^{6}\times 2\left(-3a^{2}\right)^{3}$$

Multiply 3 and 4 to get 12.

$$12a^{6}\times 2\left(-3a^{2}\right)^{3}$$

Multiply 12 and 2 to get 24.

$$24a^{6}\left(-3a^{2}\right)^{3}$$

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

$$24a^{6}\left(-3\right)^{3}\left(a^{2}\right)^{3}$$

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

$$24a^{6}\left(-3\right)^{3}a^{6}$$

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

$$24a^{6}\left(-27\right)a^{6}$$

Multiply 24 and -27 to get -648.

$$-648a^{6}a^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$-648a^{12}$$