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

$$( 3 a ^ { 3 } ) ^ { 2 } ( - 2 a b ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-72b^{6}a^{9}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

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

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

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

Calculate -2 to the power of 3 and get -8.

$$9a^{6}\left(-8\right)a^{3}b^{6}$$

Multiply 9 and -8 to get -72.

$$-72a^{6}a^{3}b^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$-72a^{9}b^{6}$$

Expand

$$-72b^{6}a^{9}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

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

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

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

Calculate -2 to the power of 3 and get -8.

$$9a^{6}\left(-8\right)a^{3}b^{6}$$

Multiply 9 and -8 to get -72.

$$-72a^{6}a^{3}b^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$-72a^{9}b^{6}$$