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

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

Evaluate

$$-24a^{10}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

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

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

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

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

Calculate -2 to the power of 3 and get -8.

$$3a^{4}\left(-8\right)a^{6}$$

Multiply 3 and -8 to get -24.

$$-24a^{4}a^{6}$$

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

$$-24a^{10}$$

Expand

$$-24a^{10}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

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

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

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

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

Calculate -2 to the power of 3 and get -8.

$$3a^{4}\left(-8\right)a^{6}$$

Multiply 3 and -8 to get -24.

$$-24a^{4}a^{6}$$

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

$$-24a^{10}$$