Solve (4)(-2a)^{6}-(-2a^3)^2-[(-2a)^2]^3

$$( 4 ) ( - 2 a ) ^ { 6 } - ( - 2 a ^ { 3 } ) ^ { 2 } - [ ( - 2 a ) ^ { 2 } ] ^ { 3 }$$

Evaluate

$$188a^{6}$$

Solution Steps

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

$$4\left(-2a\right)^{6}-\left(-2a^{3}\right)^{2}-\left(-2a\right)^{6}$$

Expand \left(-2a\right)^{6}.

$$4\left(-2\right)^{6}a^{6}-\left(-2a^{3}\right)^{2}-\left(-2a\right)^{6}$$

Calculate -2 to the power of 6 and get 64.

$$4\times 64a^{6}-\left(-2a^{3}\right)^{2}-\left(-2a\right)^{6}$$

Multiply 4 and 64 to get 256.

$$256a^{6}-\left(-2a^{3}\right)^{2}-\left(-2a\right)^{6}$$

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

$$256a^{6}-\left(-2\right)^{2}\left(a^{3}\right)^{2}-\left(-2a\right)^{6}$$

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

$$256a^{6}-\left(-2\right)^{2}a^{6}-\left(-2a\right)^{6}$$

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

$$256a^{6}-4a^{6}-\left(-2a\right)^{6}$$

Combine 256a^{6} and -4a^{6} to get 252a^{6}.

$$252a^{6}-\left(-2a\right)^{6}$$

Expand \left(-2a\right)^{6}.

$$252a^{6}-\left(-2\right)^{6}a^{6}$$

Calculate -2 to the power of 6 and get 64.

$$252a^{6}-64a^{6}$$

Combine 252a^{6} and -64a^{6} to get 188a^{6}.

$$188a^{6}$$

Expand

$$188a^{6}$$

Solution Steps

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

$$4\left(-2a\right)^{6}-\left(-2a^{3}\right)^{2}-\left(-2a\right)^{6}$$

Expand \left(-2a\right)^{6}.

$$4\left(-2\right)^{6}a^{6}-\left(-2a^{3}\right)^{2}-\left(-2a\right)^{6}$$

Calculate -2 to the power of 6 and get 64.

$$4\times 64a^{6}-\left(-2a^{3}\right)^{2}-\left(-2a\right)^{6}$$

Multiply 4 and 64 to get 256.

$$256a^{6}-\left(-2a^{3}\right)^{2}-\left(-2a\right)^{6}$$

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

$$256a^{6}-\left(-2\right)^{2}\left(a^{3}\right)^{2}-\left(-2a\right)^{6}$$

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

$$256a^{6}-\left(-2\right)^{2}a^{6}-\left(-2a\right)^{6}$$

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

$$256a^{6}-4a^{6}-\left(-2a\right)^{6}$$

Combine 256a^{6} and -4a^{6} to get 252a^{6}.

$$252a^{6}-\left(-2a\right)^{6}$$

Expand \left(-2a\right)^{6}.

$$252a^{6}-\left(-2\right)^{6}a^{6}$$

Calculate -2 to the power of 6 and get 64.

$$252a^{6}-64a^{6}$$

Combine 252a^{6} and -64a^{6} to get 188a^{6}.

$$188a^{6}$$