Solve (3fg^4)^3(fg)^3

$$( 3 f g ^ { 4 } ) ^ { 3 } ( f g ) ^ { 3 }$$

Evaluate

$$27f^{6}g^{15}$$

Solution Steps

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

$$3^{3}f^{3}\left(g^{4}\right)^{3}\left(fg\right)^{3}$$

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

$$3^{3}f^{3}g^{12}\left(fg\right)^{3}$$

Calculate 3 to the power of 3 and get 27.

$$27f^{3}g^{12}\left(fg\right)^{3}$$

Expand \left(fg\right)^{3}.

$$27f^{3}g^{12}f^{3}g^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$27f^{6}g^{12}g^{3}$$

To multiply powers of the same base, add their exponents. Add 12 and 3 to get 15.

$$27f^{6}g^{15}$$

Expand

$$27f^{6}g^{15}$$

Solution Steps

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

$$3^{3}f^{3}\left(g^{4}\right)^{3}\left(fg\right)^{3}$$

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

$$3^{3}f^{3}g^{12}\left(fg\right)^{3}$$

Calculate 3 to the power of 3 and get 27.

$$27f^{3}g^{12}\left(fg\right)^{3}$$

Expand \left(fg\right)^{3}.

$$27f^{3}g^{12}f^{3}g^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$27f^{6}g^{12}g^{3}$$

To multiply powers of the same base, add their exponents. Add 12 and 3 to get 15.

$$27f^{6}g^{15}$$