Solve a^{4}*(-3a^3)^2-(-4a^5)^2

$$a ^ { 4 } \cdot ( - 3 a ^ { 3 } ) ^ { 2 } - ( - 4 a ^ { 5 } ) ^ { 2 }$$

Evaluate

$$-7a^{10}$$

Solution Steps

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

$$a^{4}\left(-3\right)^{2}\left(a^{3}\right)^{2}-\left(-4a^{5}\right)^{2}$$

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

$$a^{4}\left(-3\right)^{2}a^{6}-\left(-4a^{5}\right)^{2}$$

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

$$a^{4}\times 9a^{6}-\left(-4a^{5}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$a^{10}\times 9-\left(-4a^{5}\right)^{2}$$

Expand \left(-4a^{5}\right)^{2}.

$$a^{10}\times 9-\left(-4\right)^{2}\left(a^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$a^{10}\times 9-\left(-4\right)^{2}a^{10}$$

Calculate -4 to the power of 2 and get 16.

$$a^{10}\times 9-16a^{10}$$

Combine a^{10}\times 9 and -16a^{10} to get -7a^{10}.

$$-7a^{10}$$

Expand

$$-7a^{10}$$

Solution Steps

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

$$a^{4}\left(-3\right)^{2}\left(a^{3}\right)^{2}-\left(-4a^{5}\right)^{2}$$

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

$$a^{4}\left(-3\right)^{2}a^{6}-\left(-4a^{5}\right)^{2}$$

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

$$a^{4}\times 9a^{6}-\left(-4a^{5}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$a^{10}\times 9-\left(-4a^{5}\right)^{2}$$

Expand \left(-4a^{5}\right)^{2}.

$$a^{10}\times 9-\left(-4\right)^{2}\left(a^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$a^{10}\times 9-\left(-4\right)^{2}a^{10}$$

Calculate -4 to the power of 2 and get 16.

$$a^{10}\times 9-16a^{10}$$

Combine a^{10}\times 9 and -16a^{10} to get -7a^{10}.

$$-7a^{10}$$