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

$$( - 3 a ^ { 2 } b c ) ^ { 2 } \cdot ( - 2 a b ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-72c^{2}a^{7}b^{8}$$

Solution Steps

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

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

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

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

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

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

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

$$9a^{4}b^{2}c^{2}\left(-2\right)^{3}a^{3}\left(b^{2}\right)^{3}$$

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

$$9a^{4}b^{2}c^{2}\left(-2\right)^{3}a^{3}b^{6}$$

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

$$9a^{4}b^{2}c^{2}\left(-8\right)a^{3}b^{6}$$

Multiply 9 and -8 to get -72.

$$-72a^{4}b^{2}c^{2}a^{3}b^{6}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$-72a^{7}b^{2}c^{2}b^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$-72a^{7}b^{8}c^{2}$$

Expand

$$-72c^{2}a^{7}b^{8}$$

Solution Steps

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

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

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

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

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

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

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

$$9a^{4}b^{2}c^{2}\left(-2\right)^{3}a^{3}\left(b^{2}\right)^{3}$$

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

$$9a^{4}b^{2}c^{2}\left(-2\right)^{3}a^{3}b^{6}$$

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

$$9a^{4}b^{2}c^{2}\left(-8\right)a^{3}b^{6}$$

Multiply 9 and -8 to get -72.

$$-72a^{4}b^{2}c^{2}a^{3}b^{6}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$-72a^{7}b^{2}c^{2}b^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$-72a^{7}b^{8}c^{2}$$