Solve (-2a^{2})^2*a^4-(a^4)^2

$$( - 2 a ^ { 2 } ) ^ { 2 } \cdot a ^ { 4 } - ( a ^ { 4 } ) ^ { 2 }$$

Evaluate

$$3a^{8}$$

Solution Steps

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

$$\left(-2a^{2}\right)^{2}a^{4}-a^{8}$$

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

$$\left(-2\right)^{2}\left(a^{2}\right)^{2}a^{4}-a^{8}$$

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

$$\left(-2\right)^{2}a^{4}a^{4}-a^{8}$$

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

$$4a^{4}a^{4}-a^{8}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$4a^{8}-a^{8}$$

Combine 4a^{8} and -a^{8} to get 3a^{8}.

$$3a^{8}$$

Expand

$$3a^{8}$$

Solution Steps

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

$$\left(-2a^{2}\right)^{2}a^{4}-a^{8}$$

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

$$\left(-2\right)^{2}\left(a^{2}\right)^{2}a^{4}-a^{8}$$

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

$$\left(-2\right)^{2}a^{4}a^{4}-a^{8}$$

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

$$4a^{4}a^{4}-a^{8}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$4a^{8}-a^{8}$$

Combine 4a^{8} and -a^{8} to get 3a^{8}.

$$3a^{8}$$