Solve sqrt{asqrt[6]{a}}:sqrt[6]{sqrt{a}}=(sqrt{a^-3})^-1:x

$$\sqrt { a \sqrt[ 6 ] { a } } : \sqrt[ 6 ] { \sqrt { a } } = ( \sqrt { a ^ { - 3 } } ) ^ { - 1 } : x$$

Solve for x

$$x=a$$

$$a>0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$xa^{-\frac{1}{12}}\sqrt{a\sqrt[6]{a}}=\left(\sqrt{a^{-3}}\right)^{-1}$$

Reorder the terms.

$$a^{-\frac{1}{12}}\sqrt{\sqrt[6]{a}a}x=\frac{1}{\sqrt{a^{-3}}}$$

The equation is in standard form.

$$\frac{\sqrt{\sqrt[6]{a}a}}{\sqrt[12]{a}}x=\frac{1}{\sqrt{\frac{1}{a^{3}}}}$$

Divide both sides by a^{-\frac{1}{12}}\sqrt{\sqrt[6]{a}a}.

$$\frac{\frac{\sqrt{\sqrt[6]{a}a}}{\sqrt[12]{a}}x\sqrt[12]{a}}{\sqrt{\sqrt[6]{a}a}}=\frac{a^{\frac{3}{2}}\sqrt[12]{a}}{\sqrt{\sqrt[6]{a}a}}$$

Dividing by a^{-\frac{1}{12}}\sqrt{\sqrt[6]{a}a} undoes the multiplication by a^{-\frac{1}{12}}\sqrt{\sqrt[6]{a}a}.

$$x=\frac{a^{\frac{3}{2}}\sqrt[12]{a}}{\sqrt{\sqrt[6]{a}a}}$$

Divide a^{\frac{3}{2}} by a^{-\frac{1}{12}}\sqrt{\sqrt[6]{a}a}.

$$x=a$$

Variable x cannot be equal to 0.

$$x=a\text{, }x\neq 0$$

Solve for a

$$a=x$$

$$x>0$$