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

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

Evaluate

$$6a^{6}$$

Solution Steps

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

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

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

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

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

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

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

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

Calculate 2 to the power of 3 and get 8.

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

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

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

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

$$6a^{6}$$

Expand

$$6a^{6}$$

Solution Steps

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

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

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

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

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

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

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

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

Calculate 2 to the power of 3 and get 8.

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

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

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

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

$$6a^{6}$$