Solve [(-3a^2b^3)^3]^2=

$$[ ( - 3 a ^ { 2 } b ^ { 3 } ) ^ { 3 } ] ^ { 2 } =$$

Evaluate

$$729a^{12}b^{18}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(\left(-3\right)^{3}a^{6}b^{9}\right)^{2}$$

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

$$\left(-27a^{6}b^{9}\right)^{2}$$

Expand \left(-27a^{6}b^{9}\right)^{2}.

$$\left(-27\right)^{2}\left(a^{6}\right)^{2}\left(b^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\left(-27\right)^{2}a^{12}\left(b^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$\left(-27\right)^{2}a^{12}b^{18}$$

Calculate -27 to the power of 2 and get 729.

$$729a^{12}b^{18}$$

Expand

$$729a^{12}b^{18}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(\left(-3\right)^{3}a^{6}b^{9}\right)^{2}$$

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

$$\left(-27a^{6}b^{9}\right)^{2}$$

Expand \left(-27a^{6}b^{9}\right)^{2}.

$$\left(-27\right)^{2}\left(a^{6}\right)^{2}\left(b^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\left(-27\right)^{2}a^{12}\left(b^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$\left(-27\right)^{2}a^{12}b^{18}$$

Calculate -27 to the power of 2 and get 729.

$$729a^{12}b^{18}$$