Solve (2a^{2})^3-7a^6+a^2*a^4

$$( 2 a ^ { 2 } ) ^ { 3 } - 7 a ^ { 6 } + a ^ { 2 } \cdot a ^ { 4 }$$

Evaluate

$$2a^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\left(2a^{2}\right)^{3}-7a^{6}+a^{6}$$

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

$$2^{3}\left(a^{2}\right)^{3}-7a^{6}+a^{6}$$

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

$$2^{3}a^{6}-7a^{6}+a^{6}$$

Calculate 2 to the power of 3 and get 8.

$$8a^{6}-7a^{6}+a^{6}$$

Combine 8a^{6} and -7a^{6} to get a^{6}.

$$a^{6}+a^{6}$$

Combine a^{6} and a^{6} to get 2a^{6}.

$$2a^{6}$$

Expand

$$2a^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\left(2a^{2}\right)^{3}-7a^{6}+a^{6}$$

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

$$2^{3}\left(a^{2}\right)^{3}-7a^{6}+a^{6}$$

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

$$2^{3}a^{6}-7a^{6}+a^{6}$$

Calculate 2 to the power of 3 and get 8.

$$8a^{6}-7a^{6}+a^{6}$$

Combine 8a^{6} and -7a^{6} to get a^{6}.

$$a^{6}+a^{6}$$

Combine a^{6} and a^{6} to get 2a^{6}.

$$2a^{6}$$