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

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

Evaluate

$$-12b^{5}a^{9}$$

Solution Steps

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

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

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

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

Multiply 3 and 4 to get 12.

$$12aa^{2}b^{2}\left(\left(-a^{2}\right)b\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$12a^{3}b^{5}\left(-a^{2}\right)^{3}$$

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

$$12a^{3}b^{5}\left(-1\right)^{3}\left(a^{2}\right)^{3}$$

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

$$12a^{3}b^{5}\left(-1\right)^{3}a^{6}$$

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

$$12a^{3}b^{5}\left(-1\right)a^{6}$$

Multiply 12 and -1 to get -12.

$$-12a^{3}b^{5}a^{6}$$

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

$$-12a^{9}b^{5}$$

Expand

$$-12b^{5}a^{9}$$

Solution Steps

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

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

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

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

Multiply 3 and 4 to get 12.

$$12aa^{2}b^{2}\left(\left(-a^{2}\right)b\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$12a^{3}b^{5}\left(-a^{2}\right)^{3}$$

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

$$12a^{3}b^{5}\left(-1\right)^{3}\left(a^{2}\right)^{3}$$

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

$$12a^{3}b^{5}\left(-1\right)^{3}a^{6}$$

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

$$12a^{3}b^{5}\left(-1\right)a^{6}$$

Multiply 12 and -1 to get -12.

$$-12a^{3}b^{5}a^{6}$$

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

$$-12a^{9}b^{5}$$