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

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

Evaluate

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

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$a^{6}-3a^{8}+\left(-2a^{3}\right)^{2}$$

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

$$a^{6}-3a^{8}+\left(-2\right)^{2}\left(a^{3}\right)^{2}$$

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

$$a^{6}-3a^{8}+\left(-2\right)^{2}a^{6}$$

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

$$a^{6}-3a^{8}+4a^{6}$$

Combine a^{6} and 4a^{6} to get 5a^{6}.

$$5a^{6}-3a^{8}$$

Expand

$$5a^{6}-3a^{8}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$a^{6}-3a^{8}+\left(-2a^{3}\right)^{2}$$

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

$$a^{6}-3a^{8}+\left(-2\right)^{2}\left(a^{3}\right)^{2}$$

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

$$a^{6}-3a^{8}+\left(-2\right)^{2}a^{6}$$

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

$$a^{6}-3a^{8}+4a^{6}$$

Combine a^{6} and 4a^{6} to get 5a^{6}.

$$5a^{6}-3a^{8}$$