Solve (-2a^2)^3*(-a)^8*(-a^4)

$$( - 2 a ^ { 2 } ) ^ { 3 } \cdot ( - a ) ^ { 8 } \cdot ( - a ^ { 4 } )$$

Evaluate

$$8a^{18}$$

Solution Steps

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

$$\left(-2\right)^{3}\left(a^{2}\right)^{3}\left(-a\right)^{8}\left(-a^{4}\right)$$

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

$$\left(-2\right)^{3}a^{6}\left(-a\right)^{8}\left(-a^{4}\right)$$

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

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

Multiply -8 and -1 to get 8.

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

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

$$8a^{10}\left(-a\right)^{8}$$

Expand \left(-a\right)^{8}.

$$8a^{10}\left(-1\right)^{8}a^{8}$$

Calculate -1 to the power of 8 and get 1.

$$8a^{10}\times 1a^{8}$$

Multiply 8 and 1 to get 8.

$$8a^{10}a^{8}$$

To multiply powers of the same base, add their exponents. Add 10 and 8 to get 18.

$$8a^{18}$$

Expand

$$8a^{18}$$

Solution Steps

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

$$\left(-2\right)^{3}\left(a^{2}\right)^{3}\left(-a\right)^{8}\left(-a^{4}\right)$$

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

$$\left(-2\right)^{3}a^{6}\left(-a\right)^{8}\left(-a^{4}\right)$$

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

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

Multiply -8 and -1 to get 8.

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

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

$$8a^{10}\left(-a\right)^{8}$$

Expand \left(-a\right)^{8}.

$$8a^{10}\left(-1\right)^{8}a^{8}$$

Calculate -1 to the power of 8 and get 1.

$$8a^{10}\times 1a^{8}$$

Multiply 8 and 1 to get 8.

$$8a^{10}a^{8}$$

To multiply powers of the same base, add their exponents. Add 10 and 8 to get 18.

$$8a^{18}$$