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

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

Evaluate

$$-4c^{2}b^{8}a^{9}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

$$4a^{6}b^{8}c^{2}\left(-1\right)^{3}a^{3}$$

Calculate -1 to the power of 3 and get -1.

$$4a^{6}b^{8}c^{2}\left(-1\right)a^{3}$$

Multiply 4 and -1 to get -4.

$$-4a^{6}b^{8}c^{2}a^{3}$$

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

$$-4a^{9}b^{8}c^{2}$$

Expand

$$-4c^{2}b^{8}a^{9}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

$$4a^{6}b^{8}c^{2}\left(-1\right)^{3}a^{3}$$

Calculate -1 to the power of 3 and get -1.

$$4a^{6}b^{8}c^{2}\left(-1\right)a^{3}$$

Multiply 4 and -1 to get -4.

$$-4a^{6}b^{8}c^{2}a^{3}$$

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

$$-4a^{9}b^{8}c^{2}$$