Solve -x=a^6*(-a^6)

$$- x = a ^ { 6 } \cdot ( - a ^ { 6 } )$$

Solve for x

$$x=a^{12}$$

Solution Steps

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

$$-x=a^{12}\left(-1\right)$$

Cancel out -1 on both sides.

$$x=a^{12}$$

Solve for a (complex solution)

$$a\in e^{\frac{\pi i}{6}}\sqrt[12]{x},\sqrt[12]{x},e^{\frac{\pi i}{3}}\sqrt[12]{x},i\sqrt[12]{x},e^{\frac{2\pi i}{3}}\sqrt[12]{x},e^{\frac{5\pi i}{6}}\sqrt[12]{x},-\sqrt[12]{x},e^{\frac{7\pi i}{6}}\sqrt[12]{x},e^{\frac{4\pi i}{3}}\sqrt[12]{x},-i\sqrt[12]{x},e^{\frac{5\pi i}{3}}\sqrt[12]{x},e^{\frac{11\pi i}{6}}\sqrt[12]{x}$$

Solve for a

$$a=\sqrt[12]{x}$$

$$a=-\sqrt[12]{x}\text{, }x\geq 0$$