Solve (2ab)^{4}(-a^{3}b)^{2}-(+3a^{2})^3(a^2b^3)^2=

$$( 2 a b ) ^ { 4 } ( - a ^ { 3 } b ) ^ { 2 } - ( + 3 a ^ { 2 } ) ^ { 3 } ( a ^ { 2 } b ^ { 3 } ) ^ { 2 } =$$

Evaluate

$$-11b^{6}a^{10}$$

Solution Steps

Expand \left(2ab\right)^{4}.

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

Calculate 2 to the power of 4 and get 16.

$$16a^{4}b^{4}\left(\left(-a^{3}\right)b\right)^{2}-\left(3a^{2}\right)^{3}\left(a^{2}b^{3}\right)^{2}$$

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

$$16a^{4}b^{4}\left(-a^{3}\right)^{2}b^{2}-\left(3a^{2}\right)^{3}\left(a^{2}b^{3}\right)^{2}$$

Calculate -a^{3} to the power of 2 and get \left(a^{3}\right)^{2}.

$$16a^{4}b^{4}\left(a^{3}\right)^{2}b^{2}-\left(3a^{2}\right)^{3}\left(a^{2}b^{3}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-\left(3a^{2}\right)^{3}\left(a^{2}b^{3}\right)^{2}$$

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

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-3^{3}\left(a^{2}\right)^{3}\left(a^{2}b^{3}\right)^{2}$$

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

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-3^{3}a^{6}\left(a^{2}b^{3}\right)^{2}$$

Calculate 3 to the power of 3 and get 27.

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-27a^{6}\left(a^{2}b^{3}\right)^{2}$$

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

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-27a^{6}\left(a^{2}\right)^{2}\left(b^{3}\right)^{2}$$

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

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-27a^{6}a^{4}\left(b^{3}\right)^{2}$$

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

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-27a^{6}a^{4}b^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-27a^{10}b^{6}$$

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

$$16a^{4}b^{6}a^{6}-27a^{10}b^{6}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$16a^{10}b^{6}-27a^{10}b^{6}$$

Combine 16a^{10}b^{6} and -27a^{10}b^{6} to get -11a^{10}b^{6}.

$$-11a^{10}b^{6}$$

Expand

$$-11b^{6}a^{10}$$

Solution Steps

Expand \left(2ab\right)^{4}.

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

Calculate 2 to the power of 4 and get 16.

$$16a^{4}b^{4}\left(\left(-a^{3}\right)b\right)^{2}-\left(3a^{2}\right)^{3}\left(a^{2}b^{3}\right)^{2}$$

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

$$16a^{4}b^{4}\left(-a^{3}\right)^{2}b^{2}-\left(3a^{2}\right)^{3}\left(a^{2}b^{3}\right)^{2}$$

Calculate -a^{3} to the power of 2 and get \left(a^{3}\right)^{2}.

$$16a^{4}b^{4}\left(a^{3}\right)^{2}b^{2}-\left(3a^{2}\right)^{3}\left(a^{2}b^{3}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-\left(3a^{2}\right)^{3}\left(a^{2}b^{3}\right)^{2}$$

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

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-3^{3}\left(a^{2}\right)^{3}\left(a^{2}b^{3}\right)^{2}$$

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

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-3^{3}a^{6}\left(a^{2}b^{3}\right)^{2}$$

Calculate 3 to the power of 3 and get 27.

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-27a^{6}\left(a^{2}b^{3}\right)^{2}$$

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

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-27a^{6}\left(a^{2}\right)^{2}\left(b^{3}\right)^{2}$$

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

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-27a^{6}a^{4}\left(b^{3}\right)^{2}$$

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

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-27a^{6}a^{4}b^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$16a^{4}b^{6}\left(a^{3}\right)^{2}-27a^{10}b^{6}$$

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

$$16a^{4}b^{6}a^{6}-27a^{10}b^{6}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$16a^{10}b^{6}-27a^{10}b^{6}$$

Combine 16a^{10}b^{6} and -27a^{10}b^{6} to get -11a^{10}b^{6}.

$$-11a^{10}b^{6}$$