Solve a^{3}a^{4}a+(a^2)^4-(2a^4)^2

$$a ^ { 3 } a ^ { 4 } a + ( a ^ { 2 } ) ^ { 4 } - ( 2 a ^ { 4 } ) ^ { 2 }$$

Evaluate

$$-2a^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$a^{7}a+\left(a^{2}\right)^{4}-\left(2a^{4}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

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

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

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

Combine a^{8} and a^{8} to get 2a^{8}.

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Combine 2a^{8} and -4a^{8} to get -2a^{8}.

$$-2a^{8}$$

Expand

$$-2a^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$a^{7}a+\left(a^{2}\right)^{4}-\left(2a^{4}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

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

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

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

Combine a^{8} and a^{8} to get 2a^{8}.

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Combine 2a^{8} and -4a^{8} to get -2a^{8}.

$$-2a^{8}$$