Solve 2a^3*(-a)^2-(-a^2)^3*(-7a)

$$2 a ^ { 3 } \cdot ( - a ) ^ { 2 } - ( - a ^ { 2 } ) ^ { 3 } \cdot ( - 7 a )$$

Evaluate

$$\left(2-7a^{2}\right)a^{5}$$

Solution Steps

Calculate -a to the power of 2 and get a^{2}.

$$2a^{3}a^{2}-\left(-a^{2}\right)^{3}\left(-7\right)a$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$2a^{5}-\left(-a^{2}\right)^{3}\left(-7\right)a$$

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

$$2a^{5}-\left(-1\right)^{3}\left(a^{2}\right)^{3}\left(-7\right)a$$

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

$$2a^{5}-\left(-1\right)^{3}a^{6}\left(-7\right)a$$

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

$$2a^{5}-\left(-a^{6}\left(-7\right)a\right)$$

Multiply -1 and -1 to get 1.

$$2a^{5}+a^{6}\left(-7\right)a$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$2a^{5}+a^{7}\left(-7\right)$$

Expand

$$2a^{5}-7a^{7}$$

Solution Steps

Calculate -a to the power of 2 and get a^{2}.

$$2a^{3}a^{2}-\left(-a^{2}\right)^{3}\left(-7\right)a$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$2a^{5}-\left(-a^{2}\right)^{3}\left(-7\right)a$$

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

$$2a^{5}-\left(-1\right)^{3}\left(a^{2}\right)^{3}\left(-7\right)a$$

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

$$2a^{5}-\left(-1\right)^{3}a^{6}\left(-7\right)a$$

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

$$2a^{5}-\left(-a^{6}\left(-7\right)a\right)$$

Multiply -1 and -1 to get 1.

$$2a^{5}+a^{6}\left(-7\right)a$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$2a^{5}+a^{7}\left(-7\right)$$