Solve (-a^{2})^3*(-a)^2*(a^4)^2=

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

Evaluate

$$-a^{16}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$\left(-a^{2}\right)^{3}a^{10}$$

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

$$\left(-1\right)^{3}\left(a^{2}\right)^{3}a^{10}$$

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

$$\left(-1\right)^{3}a^{6}a^{10}$$

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

$$-a^{6}a^{10}$$

To multiply powers of the same base, add their exponents. Add 6 and 10 to get 16.

$$-a^{16}$$

Expand

$$-a^{16}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$\left(-a^{2}\right)^{3}a^{10}$$

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

$$\left(-1\right)^{3}\left(a^{2}\right)^{3}a^{10}$$

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

$$\left(-1\right)^{3}a^{6}a^{10}$$

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

$$-a^{6}a^{10}$$

To multiply powers of the same base, add their exponents. Add 6 and 10 to get 16.

$$-a^{16}$$