Solve [-3a^{4}(-a^{2})^{2}]*(-3a^{7})+21a^6*(-7a^5)*(12a^3+16a^2)

$$[ - 3 a ^ { 4 } ( - a ^ { 2 } ) ^ { 2 } ] \cdot ( - 3 a ^ { 7 } ) + 21 a ^ { 6 } \cdot ( - 7 a ^ { 5 } ) \cdot ( 12 a ^ { 3 } + 16 a ^ { 2 } )$$

Evaluate

$$3\left(3a^{2}-588a-784\right)a^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$-3a^{11}\left(-a^{2}\right)^{2}\left(-3\right)+21a^{6}\left(-7\right)a^{5}\left(12a^{3}+16a^{2}\right)$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$-3a^{11}\left(-a^{2}\right)^{2}\left(-3\right)+21a^{11}\left(-7\right)\left(12a^{3}+16a^{2}\right)$$

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

$$-3a^{11}\left(a^{2}\right)^{2}\left(-3\right)+21a^{11}\left(-7\right)\left(12a^{3}+16a^{2}\right)$$

Multiply -3 and -3 to get 9.

$$9a^{11}\left(a^{2}\right)^{2}+21a^{11}\left(-7\right)\left(12a^{3}+16a^{2}\right)$$

Multiply 21 and -7 to get -147.

$$9a^{11}\left(a^{2}\right)^{2}-147a^{11}\left(12a^{3}+16a^{2}\right)$$

Use the distributive property to multiply -147a^{11} by 12a^{3}+16a^{2}.

$$9a^{11}\left(a^{2}\right)^{2}-1764a^{14}-2352a^{13}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$9a^{11}a^{4}-1764a^{14}-2352a^{13}$$

To multiply powers of the same base, add their exponents. Add 11 and 4 to get 15.

$$9a^{15}-1764a^{14}-2352a^{13}$$

Expand

$$9a^{15}-1764a^{14}-2352a^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$-3a^{11}\left(-a^{2}\right)^{2}\left(-3\right)+21a^{6}\left(-7\right)a^{5}\left(12a^{3}+16a^{2}\right)$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$-3a^{11}\left(-a^{2}\right)^{2}\left(-3\right)+21a^{11}\left(-7\right)\left(12a^{3}+16a^{2}\right)$$

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

$$-3a^{11}\left(a^{2}\right)^{2}\left(-3\right)+21a^{11}\left(-7\right)\left(12a^{3}+16a^{2}\right)$$

Multiply -3 and -3 to get 9.

$$9a^{11}\left(a^{2}\right)^{2}+21a^{11}\left(-7\right)\left(12a^{3}+16a^{2}\right)$$

Multiply 21 and -7 to get -147.

$$9a^{11}\left(a^{2}\right)^{2}-147a^{11}\left(12a^{3}+16a^{2}\right)$$

Use the distributive property to multiply -147a^{11} by 12a^{3}+16a^{2}.

$$9a^{11}\left(a^{2}\right)^{2}-1764a^{14}-2352a^{13}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$9a^{11}a^{4}-1764a^{14}-2352a^{13}$$

To multiply powers of the same base, add their exponents. Add 11 and 4 to get 15.

$$9a^{15}-1764a^{14}-2352a^{13}$$