Solve (-2g^3h)(-3gJ^4)^2(-9hJ)^2

$$( - 2 g ^ { 3 } h ) ( - 3 g J ^ { 4 } ) ^ { 2 } ( - 9 h J ) ^ { 2 }$$

Evaluate

$$-1458h^{3}g^{5}J^{10}$$

Solution Steps

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

$$-2g^{3}h\left(-3\right)^{2}g^{2}\left(J^{4}\right)^{2}\left(-9hJ\right)^{2}$$

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

$$-2g^{3}h\left(-3\right)^{2}g^{2}J^{8}\left(-9hJ\right)^{2}$$

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

$$-2g^{3}h\times 9g^{2}J^{8}\left(-9hJ\right)^{2}$$

Multiply -2 and 9 to get -18.

$$-18g^{3}hg^{2}J^{8}\left(-9hJ\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-18g^{5}hJ^{8}\left(-9hJ\right)^{2}$$

Expand \left(-9hJ\right)^{2}.

$$-18g^{5}hJ^{8}\left(-9\right)^{2}h^{2}J^{2}$$

Calculate -9 to the power of 2 and get 81.

$$-18g^{5}hJ^{8}\times 81h^{2}J^{2}$$

Multiply -18 and 81 to get -1458.

$$-1458g^{5}hJ^{8}h^{2}J^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-1458g^{5}h^{3}J^{8}J^{2}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$-1458g^{5}h^{3}J^{10}$$

Expand

$$-1458h^{3}g^{5}J^{10}$$

Solution Steps

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

$$-2g^{3}h\left(-3\right)^{2}g^{2}\left(J^{4}\right)^{2}\left(-9hJ\right)^{2}$$

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

$$-2g^{3}h\left(-3\right)^{2}g^{2}J^{8}\left(-9hJ\right)^{2}$$

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

$$-2g^{3}h\times 9g^{2}J^{8}\left(-9hJ\right)^{2}$$

Multiply -2 and 9 to get -18.

$$-18g^{3}hg^{2}J^{8}\left(-9hJ\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-18g^{5}hJ^{8}\left(-9hJ\right)^{2}$$

Expand \left(-9hJ\right)^{2}.

$$-18g^{5}hJ^{8}\left(-9\right)^{2}h^{2}J^{2}$$

Calculate -9 to the power of 2 and get 81.

$$-18g^{5}hJ^{8}\times 81h^{2}J^{2}$$

Multiply -18 and 81 to get -1458.

$$-1458g^{5}hJ^{8}h^{2}J^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-1458g^{5}h^{3}J^{8}J^{2}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$-1458g^{5}h^{3}J^{10}$$