Solve frac{ax^frac{n{2}}}{2}*b=frac{4sqrt{3}}{2}

$$\frac { a x ^ { \frac { n } { 2 } } } { 2 } \times b = \frac { 4 \sqrt { 3 } } { 2 }$$

Solve for a (complex solution)

$$a=\frac{4\sqrt{3}x^{-\frac{n}{2}}}{b}$$

$$b\neq 0\text{ and }\left(n=0\text{ or }x\neq 0\right)$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$ax^{\frac{n}{2}}b=4\sqrt{3}$$

Reorder the terms.

$$abx^{\frac{n}{2}}=4\sqrt{3}$$

The equation is in standard form.

$$bx^{\frac{n}{2}}a=4\sqrt{3}$$

Divide both sides by bx^{\frac{1}{2}n}.

$$\frac{bx^{\frac{n}{2}}a}{bx^{\frac{n}{2}}}=\frac{4\sqrt{3}}{bx^{\frac{n}{2}}}$$

Dividing by bx^{\frac{1}{2}n} undoes the multiplication by bx^{\frac{1}{2}n}.

$$a=\frac{4\sqrt{3}}{bx^{\frac{n}{2}}}$$

Divide 4\sqrt{3} by bx^{\frac{1}{2}n}.

$$a=\frac{4\sqrt{3}x^{-\frac{n}{2}}}{b}$$

Solve for b (complex solution)

$$b=\frac{4\sqrt{3}x^{-\frac{n}{2}}}{a}$$

$$\left(n=0\text{ or }x\neq 0\right)\text{ and }a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$ax^{\frac{n}{2}}b=4\sqrt{3}$$

Divide both sides by ax^{\frac{1}{2}n}.

$$\frac{ax^{\frac{n}{2}}b}{ax^{\frac{n}{2}}}=\frac{4\sqrt{3}}{ax^{\frac{n}{2}}}$$

Dividing by ax^{\frac{1}{2}n} undoes the multiplication by ax^{\frac{1}{2}n}.

$$b=\frac{4\sqrt{3}}{ax^{\frac{n}{2}}}$$

Divide 4\sqrt{3} by ax^{\frac{1}{2}n}.

$$b=\frac{4\sqrt{3}x^{-\frac{n}{2}}}{a}$$

Solve for a

$$a=\frac{4\sqrt{3}x^{-\frac{n}{2}}}{b}$$

$$\left(x>0\text{ and }b\neq 0\right)\text{ or }\left(x<0\text{ and }Denominator(-\frac{n}{2})\text{bmod}2=1\text{ and }b\neq 0\text{ and }Denominator(\frac{n}{2})\text{bmod}2=1\right)$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$ax^{\frac{n}{2}}b=4\sqrt{3}$$

Reorder the terms.

$$abx^{\frac{n}{2}}=4\sqrt{3}$$

The equation is in standard form.

$$bx^{\frac{n}{2}}a=4\sqrt{3}$$

Divide both sides by bx^{\frac{1}{2}n}.

$$\frac{bx^{\frac{n}{2}}a}{bx^{\frac{n}{2}}}=\frac{4\sqrt{3}}{bx^{\frac{n}{2}}}$$

Dividing by bx^{\frac{1}{2}n} undoes the multiplication by bx^{\frac{1}{2}n}.

$$a=\frac{4\sqrt{3}}{bx^{\frac{n}{2}}}$$

Divide 4\sqrt{3} by bx^{\frac{1}{2}n}.

$$a=\frac{4\sqrt{3}x^{-\frac{n}{2}}}{b}$$

Solve for b

$$b=\frac{4\sqrt{3}x^{-\frac{n}{2}}}{a}$$

$$\left(a\neq 0\text{ and }x>0\right)\text{ or }\left(a\neq 0\text{ and }x<0\text{ and }Denominator(-\frac{n}{2})\text{bmod}2=1\text{ and }Denominator(\frac{n}{2})\text{bmod}2=1\right)$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$ax^{\frac{n}{2}}b=4\sqrt{3}$$

Divide both sides by ax^{\frac{1}{2}n}.

$$\frac{ax^{\frac{n}{2}}b}{ax^{\frac{n}{2}}}=\frac{4\sqrt{3}}{ax^{\frac{n}{2}}}$$

Dividing by ax^{\frac{1}{2}n} undoes the multiplication by ax^{\frac{1}{2}n}.

$$b=\frac{4\sqrt{3}}{ax^{\frac{n}{2}}}$$

Divide 4\sqrt{3} by ax^{\frac{1}{2}n}.

$$b=\frac{4\sqrt{3}x^{-\frac{n}{2}}}{a}$$