Solve (-2a^{2})^2*a^4-(5a^4)^2

$$( - 2 a ^ { 2 } ) ^ { 2 } \cdot a ^ { 4 } - ( 5 a ^ { 4 } ) ^ { 2 }$$

Evaluate

$$-21a^{8}$$

Solution Steps

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

$$\left(-2\right)^{2}\left(a^{2}\right)^{2}a^{4}-\left(5a^{4}\right)^{2}$$

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

$$\left(-2\right)^{2}a^{4}a^{4}-\left(5a^{4}\right)^{2}$$

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

$$4a^{4}a^{4}-\left(5a^{4}\right)^{2}$$

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

$$4a^{8}-\left(5a^{4}\right)^{2}$$

Expand \left(5a^{4}\right)^{2}.

$$4a^{8}-5^{2}\left(a^{4}\right)^{2}$$

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

$$4a^{8}-5^{2}a^{8}$$

Calculate 5 to the power of 2 and get 25.

$$4a^{8}-25a^{8}$$

Combine 4a^{8} and -25a^{8} to get -21a^{8}.

$$-21a^{8}$$

Expand

$$-21a^{8}$$

Solution Steps

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

$$\left(-2\right)^{2}\left(a^{2}\right)^{2}a^{4}-\left(5a^{4}\right)^{2}$$

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

$$\left(-2\right)^{2}a^{4}a^{4}-\left(5a^{4}\right)^{2}$$

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

$$4a^{4}a^{4}-\left(5a^{4}\right)^{2}$$

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

$$4a^{8}-\left(5a^{4}\right)^{2}$$

Expand \left(5a^{4}\right)^{2}.

$$4a^{8}-5^{2}\left(a^{4}\right)^{2}$$

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

$$4a^{8}-5^{2}a^{8}$$

Calculate 5 to the power of 2 and get 25.

$$4a^{8}-25a^{8}$$

Combine 4a^{8} and -25a^{8} to get -21a^{8}.

$$-21a^{8}$$