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

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

Evaluate

$$-9a^{6}$$

Solution Steps

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

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

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

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

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

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

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

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

Calculate -3 to the power of 2 and get 9.

$$64a^{6}-9a^{6}+\left(-\left(2a\right)^{2}\right)^{3}$$

Combine 64a^{6} and -9a^{6} to get 55a^{6}.

$$55a^{6}+\left(-\left(2a\right)^{2}\right)^{3}$$

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

$$55a^{6}+\left(-2^{2}a^{2}\right)^{3}$$

Calculate 2 to the power of 2 and get 4.

$$55a^{6}+\left(-4a^{2}\right)^{3}$$

Expand \left(-4a^{2}\right)^{3}.

$$55a^{6}+\left(-4\right)^{3}\left(a^{2}\right)^{3}$$

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

$$55a^{6}+\left(-4\right)^{3}a^{6}$$

Calculate -4 to the power of 3 and get -64.

$$55a^{6}-64a^{6}$$

Combine 55a^{6} and -64a^{6} to get -9a^{6}.

$$-9a^{6}$$

Expand

$$-9a^{6}$$

Solution Steps

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

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

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

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

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

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

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

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

Calculate -3 to the power of 2 and get 9.

$$64a^{6}-9a^{6}+\left(-\left(2a\right)^{2}\right)^{3}$$

Combine 64a^{6} and -9a^{6} to get 55a^{6}.

$$55a^{6}+\left(-\left(2a\right)^{2}\right)^{3}$$

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

$$55a^{6}+\left(-2^{2}a^{2}\right)^{3}$$

Calculate 2 to the power of 2 and get 4.

$$55a^{6}+\left(-4a^{2}\right)^{3}$$

Expand \left(-4a^{2}\right)^{3}.

$$55a^{6}+\left(-4\right)^{3}\left(a^{2}\right)^{3}$$

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

$$55a^{6}+\left(-4\right)^{3}a^{6}$$

Calculate -4 to the power of 3 and get -64.

$$55a^{6}-64a^{6}$$

Combine 55a^{6} and -64a^{6} to get -9a^{6}.

$$-9a^{6}$$