Solve (-2a^2)^3=-8a^6

$$( - 2 a ^ { 2 } ) ^ { 3 } = - 8 a ^ { 6 }$$

Solve for a

$$a\in \mathrm{R}$$

Solution Steps

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

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

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

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

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

$$-8a^{6}=-8a^{6}$$

Add 8a^{6} to both sides.

$$-8a^{6}+8a^{6}=0$$

Combine -8a^{6} and 8a^{6} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{R}$$