Solve (-2^{2}a^{2})(-b^{2})^3+(-3a)^2(-b^3)^2=

$$( - 2 ^ { 2 } a ^ { 2 } ) ( - b ^ { 2 } ) ^ { 3 } + ( - 3 a ) ^ { 2 } ( - b ^ { 3 } ) ^ { 2 } =$$

Evaluate

$$13a^{2}b^{6}$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

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

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

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

$$-4a^{2}\left(-b^{2}\right)^{3}+9a^{2}\left(-b^{3}\right)^{2}$$

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

$$-4a^{2}\left(-b^{2}\right)^{3}+9a^{2}\left(b^{3}\right)^{2}$$

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

$$-4a^{2}\left(-b^{2}\right)^{3}+9a^{2}b^{6}$$

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

$$-4a^{2}\left(-1\right)^{3}\left(b^{2}\right)^{3}+9a^{2}b^{6}$$

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

$$-4a^{2}\left(-1\right)^{3}b^{6}+9a^{2}b^{6}$$

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

$$-4a^{2}\left(-1\right)b^{6}+9a^{2}b^{6}$$

Multiply -4 and -1 to get 4.

$$4a^{2}b^{6}+9a^{2}b^{6}$$

Combine 4a^{2}b^{6} and 9a^{2}b^{6} to get 13a^{2}b^{6}.

$$13a^{2}b^{6}$$

Expand

$$13a^{2}b^{6}$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

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

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

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

$$-4a^{2}\left(-b^{2}\right)^{3}+9a^{2}\left(-b^{3}\right)^{2}$$

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

$$-4a^{2}\left(-b^{2}\right)^{3}+9a^{2}\left(b^{3}\right)^{2}$$

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

$$-4a^{2}\left(-b^{2}\right)^{3}+9a^{2}b^{6}$$

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

$$-4a^{2}\left(-1\right)^{3}\left(b^{2}\right)^{3}+9a^{2}b^{6}$$

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

$$-4a^{2}\left(-1\right)^{3}b^{6}+9a^{2}b^{6}$$

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

$$-4a^{2}\left(-1\right)b^{6}+9a^{2}b^{6}$$

Multiply -4 and -1 to get 4.

$$4a^{2}b^{6}+9a^{2}b^{6}$$

Combine 4a^{2}b^{6} and 9a^{2}b^{6} to get 13a^{2}b^{6}.

$$13a^{2}b^{6}$$