Solve (-a^2)^3*[(-a)^3]^2

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

Evaluate

$$-a^{12}$$

Solution Steps

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

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

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

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

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

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

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

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

Expand \left(-a\right)^{6}.

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

Calculate -1 to the power of 6 and get 1.

$$-a^{6}a^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$-a^{12}$$

Expand

$$-a^{12}$$

Solution Steps

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

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

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

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

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

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

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

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

Expand \left(-a\right)^{6}.

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

Calculate -1 to the power of 6 and get 1.

$$-a^{6}a^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$-a^{12}$$