Solve (x^4)^-2/x*(x^-3)^3operatorname{npn}x=12

$$\frac { ( x ^ { 4 } ) ^ { - 2 } } { x \cdot ( x ^ { - 3 } ) ^ { 3 } } \operatorname { npn } x = 12$$

Solve for p

$$p=\frac{12}{xn^{2}}$$

$$x\neq 0\text{ and }n\neq 0$$

Steps for Solving Linear Equation

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

$$\frac{x^{-8}}{x\left(x^{-3}\right)^{3}}npnx=12$$

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\frac{x^{-8}}{xx^{-9}}npnx=12$$

To multiply powers of the same base, add their exponents. Add 1 and -9 to get -8.

$$\frac{x^{-8}}{x^{-8}}npnx=12$$

Multiply n and n to get n^{2}.

$$\frac{x^{-8}}{x^{-8}}n^{2}px=12$$

Cancel out x^{-8} in both numerator and denominator.

$$1n^{2}px=12$$

Reorder the terms.

$$pxn^{2}=12$$

The equation is in standard form.

$$xn^{2}p=12$$

Divide both sides by xn^{2}.

$$\frac{xn^{2}p}{xn^{2}}=\frac{12}{xn^{2}}$$

Dividing by xn^{2} undoes the multiplication by xn^{2}.

$$p=\frac{12}{xn^{2}}$$

Solve for n (complex solution)

$$n=-2\sqrt{3}p^{-\frac{1}{2}}x^{-\frac{1}{2}}$$

$$n=2\sqrt{3}p^{-\frac{1}{2}}x^{-\frac{1}{2}}\text{, }x\neq 0\text{ and }p\neq 0$$

Solve for n

$$n=2\sqrt{\frac{3}{px}}$$

$$n=-2\sqrt{\frac{3}{px}}\text{, }\left(x>0\text{ and }p>0\right)\text{ or }\left(p<0\text{ and }x<0\right)$$