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

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

Evaluate

$$a^{11}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

Multiply -1 and -1 to get 1.

$$a^{5}a^{6}$$

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

$$a^{11}$$

Expand

$$a^{11}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

Multiply -1 and -1 to get 1.

$$a^{5}a^{6}$$

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

$$a^{11}$$