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

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

Evaluate

$$47a^{6}$$

Solution Steps

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

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

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

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

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

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

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

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

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

Calculate -2 to the power of 3 and get -8.

$$55a^{6}-8a^{6}$$

Combine 55a^{6} and -8a^{6} to get 47a^{6}.

$$47a^{6}$$

Expand

$$47a^{6}$$

Solution Steps

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

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

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

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

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

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

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

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

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

Calculate -2 to the power of 3 and get -8.

$$55a^{6}-8a^{6}$$

Combine 55a^{6} and -8a^{6} to get 47a^{6}.

$$47a^{6}$$