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

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

Evaluate

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

Solution Steps

Calculate -a^{3} to the power of 2 and get \left(a^{3}\right)^{2}.

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

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

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

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

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

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

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

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

$$a^{6}\left(-1\right)^{3}b^{3}-a^{6}b^{3}$$

Calculate -1 to the power of 3 and get -1.

$$a^{6}\left(-1\right)b^{3}-a^{6}b^{3}$$

Combine a^{6}\left(-1\right)b^{3} and -a^{6}b^{3} to get -2a^{6}b^{3}.

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

Expand

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

Solution Steps

Calculate -a^{3} to the power of 2 and get \left(a^{3}\right)^{2}.

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

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

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

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

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

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

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

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

$$a^{6}\left(-1\right)^{3}b^{3}-a^{6}b^{3}$$

Calculate -1 to the power of 3 and get -1.

$$a^{6}\left(-1\right)b^{3}-a^{6}b^{3}$$

Combine a^{6}\left(-1\right)b^{3} and -a^{6}b^{3} to get -2a^{6}b^{3}.

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