Solve (2r^4)^3(-3rq)^2

$$( 2 r ^ { 4 } ) ^ { 3 } ( - 3 r q ) ^ { 2 }$$

Evaluate

$$72q^{2}r^{14}$$

Solution Steps

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

$$2^{3}\left(r^{4}\right)^{3}\left(-3rq\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$2^{3}r^{12}\left(-3rq\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8r^{12}\left(-3rq\right)^{2}$$

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

$$8r^{12}\left(-3\right)^{2}r^{2}q^{2}$$

Calculate -3 to the power of 2 and get 9.

$$8r^{12}\times 9r^{2}q^{2}$$

Multiply 8 and 9 to get 72.

$$72r^{12}r^{2}q^{2}$$

To multiply powers of the same base, add their exponents. Add 12 and 2 to get 14.

$$72r^{14}q^{2}$$

Expand

$$72q^{2}r^{14}$$

Solution Steps

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

$$2^{3}\left(r^{4}\right)^{3}\left(-3rq\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$2^{3}r^{12}\left(-3rq\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8r^{12}\left(-3rq\right)^{2}$$

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

$$8r^{12}\left(-3\right)^{2}r^{2}q^{2}$$

Calculate -3 to the power of 2 and get 9.

$$8r^{12}\times 9r^{2}q^{2}$$

Multiply 8 and 9 to get 72.

$$72r^{12}r^{2}q^{2}$$

To multiply powers of the same base, add their exponents. Add 12 and 2 to get 14.

$$72r^{14}q^{2}$$