Solve -3(-2a^{7}b^7)^2(3a^5b)^3

$$- 3 ( - 2 a ^ { 7 } b ^ { 7 } ) ^ { 2 } ( 3 a ^ { 5 } b ) ^ { 3 }$$

Evaluate

$$-324b^{17}a^{29}$$

Solution Steps

Expand \left(-2a^{7}b^{7}\right)^{2}.

$$-3\left(-2\right)^{2}\left(a^{7}\right)^{2}\left(b^{7}\right)^{2}\times \left(3a^{5}b\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$-3\left(-2\right)^{2}a^{14}\left(b^{7}\right)^{2}\times \left(3a^{5}b\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$-3\left(-2\right)^{2}a^{14}b^{14}\times \left(3a^{5}b\right)^{3}$$

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

$$-3\times 4a^{14}b^{14}\times \left(3a^{5}b\right)^{3}$$

Multiply -3 and 4 to get -12.

$$-12a^{14}b^{14}\times \left(3a^{5}b\right)^{3}$$

Expand \left(3a^{5}b\right)^{3}.

$$-12a^{14}b^{14}\times 3^{3}\left(a^{5}\right)^{3}b^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$-12a^{14}b^{14}\times 3^{3}a^{15}b^{3}$$

Calculate 3 to the power of 3 and get 27.

$$-12a^{14}b^{14}\times 27a^{15}b^{3}$$

Multiply -12 and 27 to get -324.

$$-324a^{14}b^{14}a^{15}b^{3}$$

To multiply powers of the same base, add their exponents. Add 14 and 15 to get 29.

$$-324a^{29}b^{14}b^{3}$$

To multiply powers of the same base, add their exponents. Add 14 and 3 to get 17.

$$-324a^{29}b^{17}$$

Expand

$$-324b^{17}a^{29}$$

Solution Steps

Expand \left(-2a^{7}b^{7}\right)^{2}.

$$-3\left(-2\right)^{2}\left(a^{7}\right)^{2}\left(b^{7}\right)^{2}\times \left(3a^{5}b\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$-3\left(-2\right)^{2}a^{14}\left(b^{7}\right)^{2}\times \left(3a^{5}b\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$-3\left(-2\right)^{2}a^{14}b^{14}\times \left(3a^{5}b\right)^{3}$$

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

$$-3\times 4a^{14}b^{14}\times \left(3a^{5}b\right)^{3}$$

Multiply -3 and 4 to get -12.

$$-12a^{14}b^{14}\times \left(3a^{5}b\right)^{3}$$

Expand \left(3a^{5}b\right)^{3}.

$$-12a^{14}b^{14}\times 3^{3}\left(a^{5}\right)^{3}b^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$-12a^{14}b^{14}\times 3^{3}a^{15}b^{3}$$

Calculate 3 to the power of 3 and get 27.

$$-12a^{14}b^{14}\times 27a^{15}b^{3}$$

Multiply -12 and 27 to get -324.

$$-324a^{14}b^{14}a^{15}b^{3}$$

To multiply powers of the same base, add their exponents. Add 14 and 15 to get 29.

$$-324a^{29}b^{14}b^{3}$$

To multiply powers of the same base, add their exponents. Add 14 and 3 to get 17.

$$-324a^{29}b^{17}$$