Solve 3g^4(2g^6h^2)^3

$$3 g ^ { 4 } ( 2 g ^ { 6 } h ^ { 2 } ) ^ { 3 }$$

Evaluate

$$24h^{6}g^{22}$$

Solution Steps

Expand \left(2g^{6}h^{2}\right)^{3}.

$$3g^{4}\times 2^{3}\left(g^{6}\right)^{3}\left(h^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$3g^{4}\times 2^{3}g^{18}\left(h^{2}\right)^{3}$$

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

$$3g^{4}\times 2^{3}g^{18}h^{6}$$

Calculate 2 to the power of 3 and get 8.

$$3g^{4}\times 8g^{18}h^{6}$$

Multiply 3 and 8 to get 24.

$$24g^{4}g^{18}h^{6}$$

To multiply powers of the same base, add their exponents. Add 4 and 18 to get 22.

$$24g^{22}h^{6}$$

Expand

$$24h^{6}g^{22}$$

Solution Steps

Expand \left(2g^{6}h^{2}\right)^{3}.

$$3g^{4}\times 2^{3}\left(g^{6}\right)^{3}\left(h^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$3g^{4}\times 2^{3}g^{18}\left(h^{2}\right)^{3}$$

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

$$3g^{4}\times 2^{3}g^{18}h^{6}$$

Calculate 2 to the power of 3 and get 8.

$$3g^{4}\times 8g^{18}h^{6}$$

Multiply 3 and 8 to get 24.

$$24g^{4}g^{18}h^{6}$$

To multiply powers of the same base, add their exponents. Add 4 and 18 to get 22.

$$24g^{22}h^{6}$$