Solve (-3d^{2}f^{3}g)^2[(-3d^2f)^3]^2

$$( - 3 d ^ { 2 } f ^ { 3 } g ) ^ { 2 } [ ( - 3 d ^ { 2 } f ) ^ { 3 } ] ^ { 2 }$$

Evaluate

$$6561g^{2}f^{12}d^{16}$$

Solution Steps

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

$$\left(-3d^{2}f^{3}g\right)^{2}\left(-3d^{2}f\right)^{6}$$

Expand \left(-3d^{2}f^{3}g\right)^{2}.

$$\left(-3\right)^{2}\left(d^{2}\right)^{2}\left(f^{3}\right)^{2}g^{2}\left(-3d^{2}f\right)^{6}$$

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

$$\left(-3\right)^{2}d^{4}\left(f^{3}\right)^{2}g^{2}\left(-3d^{2}f\right)^{6}$$

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

$$\left(-3\right)^{2}d^{4}f^{6}g^{2}\left(-3d^{2}f\right)^{6}$$

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

$$9d^{4}f^{6}g^{2}\left(-3d^{2}f\right)^{6}$$

Expand \left(-3d^{2}f\right)^{6}.

$$9d^{4}f^{6}g^{2}\left(-3\right)^{6}\left(d^{2}\right)^{6}f^{6}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$9d^{4}f^{6}g^{2}\left(-3\right)^{6}d^{12}f^{6}$$

Calculate -3 to the power of 6 and get 729.

$$9d^{4}f^{6}g^{2}\times 729d^{12}f^{6}$$

Multiply 9 and 729 to get 6561.

$$6561d^{4}f^{6}g^{2}d^{12}f^{6}$$

To multiply powers of the same base, add their exponents. Add 4 and 12 to get 16.

$$6561d^{16}f^{6}g^{2}f^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$6561d^{16}f^{12}g^{2}$$

Expand

$$6561g^{2}f^{12}d^{16}$$

Solution Steps

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

$$\left(-3d^{2}f^{3}g\right)^{2}\left(-3d^{2}f\right)^{6}$$

Expand \left(-3d^{2}f^{3}g\right)^{2}.

$$\left(-3\right)^{2}\left(d^{2}\right)^{2}\left(f^{3}\right)^{2}g^{2}\left(-3d^{2}f\right)^{6}$$

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

$$\left(-3\right)^{2}d^{4}\left(f^{3}\right)^{2}g^{2}\left(-3d^{2}f\right)^{6}$$

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

$$\left(-3\right)^{2}d^{4}f^{6}g^{2}\left(-3d^{2}f\right)^{6}$$

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

$$9d^{4}f^{6}g^{2}\left(-3d^{2}f\right)^{6}$$

Expand \left(-3d^{2}f\right)^{6}.

$$9d^{4}f^{6}g^{2}\left(-3\right)^{6}\left(d^{2}\right)^{6}f^{6}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$9d^{4}f^{6}g^{2}\left(-3\right)^{6}d^{12}f^{6}$$

Calculate -3 to the power of 6 and get 729.

$$9d^{4}f^{6}g^{2}\times 729d^{12}f^{6}$$

Multiply 9 and 729 to get 6561.

$$6561d^{4}f^{6}g^{2}d^{12}f^{6}$$

To multiply powers of the same base, add their exponents. Add 4 and 12 to get 16.

$$6561d^{16}f^{6}g^{2}f^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$6561d^{16}f^{12}g^{2}$$