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

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

Evaluate

$$-72b^{7}a^{14}$$

Solution Steps

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

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

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

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

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

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

Expand \left(3a^{4}b^{2}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

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

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

Calculate 3 to the power of 2 and get 9.

$$-8a^{6}b^{3}\times 9a^{8}b^{4}$$

Multiply -8 and 9 to get -72.

$$-72a^{6}b^{3}a^{8}b^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$-72a^{14}b^{3}b^{4}$$

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

$$-72a^{14}b^{7}$$

Expand

$$-72b^{7}a^{14}$$

Solution Steps

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

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

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

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

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

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

Expand \left(3a^{4}b^{2}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

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

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

Calculate 3 to the power of 2 and get 9.

$$-8a^{6}b^{3}\times 9a^{8}b^{4}$$

Multiply -8 and 9 to get -72.

$$-72a^{6}b^{3}a^{8}b^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$-72a^{14}b^{3}b^{4}$$

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

$$-72a^{14}b^{7}$$