Solve (-2t^3)^3-3(-2t^3)^4

$$( - 2 t ^ { 3 } ) ^ { 3 } - 3 ( - 2 t ^ { 3 } ) ^ { 4 }$$

Evaluate

$$-48t^{12}-8t^{9}$$

Solution Steps

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

$$\left(-2\right)^{3}\left(t^{3}\right)^{3}-3\left(-2t^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(-2\right)^{3}t^{9}-3\left(-2t^{3}\right)^{4}$$

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

$$-8t^{9}-3\left(-2t^{3}\right)^{4}$$

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

$$-8t^{9}-3\left(-2\right)^{4}\left(t^{3}\right)^{4}$$

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

$$-8t^{9}-3\left(-2\right)^{4}t^{12}$$

Calculate -2 to the power of 4 and get 16.

$$-8t^{9}-3\times 16t^{12}$$

Multiply 3 and 16 to get 48.

$$-8t^{9}-48t^{12}$$

Expand

$$-48t^{12}-8t^{9}$$

Solution Steps

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

$$\left(-2\right)^{3}\left(t^{3}\right)^{3}-3\left(-2t^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(-2\right)^{3}t^{9}-3\left(-2t^{3}\right)^{4}$$

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

$$-8t^{9}-3\left(-2t^{3}\right)^{4}$$

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

$$-8t^{9}-3\left(-2\right)^{4}\left(t^{3}\right)^{4}$$

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

$$-8t^{9}-3\left(-2\right)^{4}t^{12}$$

Calculate -2 to the power of 4 and get 16.

$$-8t^{9}-3\times 16t^{12}$$

Multiply 3 and 16 to get 48.

$$-8t^{9}-48t^{12}$$