Solve (3w^{2}r)^2(-2w^5r^2)^3

$$( 3 w ^ { 2 } r ) ^ { 2 } ( - 2 w ^ { 5 } r ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-72r^{8}w^{19}$$

Solution Steps

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

$$3^{2}\left(w^{2}\right)^{2}r^{2}\left(-2w^{5}r^{2}\right)^{3}$$

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

$$3^{2}w^{4}r^{2}\left(-2w^{5}r^{2}\right)^{3}$$

Calculate 3 to the power of 2 and get 9.

$$9w^{4}r^{2}\left(-2w^{5}r^{2}\right)^{3}$$

Expand \left(-2w^{5}r^{2}\right)^{3}.

$$9w^{4}r^{2}\left(-2\right)^{3}\left(w^{5}\right)^{3}\left(r^{2}\right)^{3}$$

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

$$9w^{4}r^{2}\left(-2\right)^{3}w^{15}\left(r^{2}\right)^{3}$$

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

$$9w^{4}r^{2}\left(-2\right)^{3}w^{15}r^{6}$$

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

$$9w^{4}r^{2}\left(-8\right)w^{15}r^{6}$$

Multiply 9 and -8 to get -72.

$$-72w^{4}r^{2}w^{15}r^{6}$$

To multiply powers of the same base, add their exponents. Add 4 and 15 to get 19.

$$-72w^{19}r^{2}r^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$-72w^{19}r^{8}$$

Expand

$$-72r^{8}w^{19}$$

Solution Steps

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

$$3^{2}\left(w^{2}\right)^{2}r^{2}\left(-2w^{5}r^{2}\right)^{3}$$

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

$$3^{2}w^{4}r^{2}\left(-2w^{5}r^{2}\right)^{3}$$

Calculate 3 to the power of 2 and get 9.

$$9w^{4}r^{2}\left(-2w^{5}r^{2}\right)^{3}$$

Expand \left(-2w^{5}r^{2}\right)^{3}.

$$9w^{4}r^{2}\left(-2\right)^{3}\left(w^{5}\right)^{3}\left(r^{2}\right)^{3}$$

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

$$9w^{4}r^{2}\left(-2\right)^{3}w^{15}\left(r^{2}\right)^{3}$$

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

$$9w^{4}r^{2}\left(-2\right)^{3}w^{15}r^{6}$$

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

$$9w^{4}r^{2}\left(-8\right)w^{15}r^{6}$$

Multiply 9 and -8 to get -72.

$$-72w^{4}r^{2}w^{15}r^{6}$$

To multiply powers of the same base, add their exponents. Add 4 and 15 to get 19.

$$-72w^{19}r^{2}r^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$-72w^{19}r^{8}$$