Solve 7:f(x)=1/8x8/-x^4

$$7 : f ( x ) = \frac { 1 } { 8 } x \frac { 8 } { - x ^ { 4 } }$$

Solve for f

$$f=-7x^{4}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Variable f cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 8f, the least common multiple of f,8.

$$8\times 7x=\frac{1}{8}x\left(-8\right)fx^{-4}\times 8$$

Multiply 8 and 7 to get 56.

$$56x=\frac{1}{8}x\left(-8\right)fx^{-4}\times 8$$

To multiply powers of the same base, add their exponents. Add 1 and -4 to get -3.

$$56x=\frac{1}{8}x^{-3}\left(-8\right)f\times 8$$

Multiply \frac{1}{8} and -8 to get -1.

$$56x=-x^{-3}f\times 8$$

Multiply -1 and 8 to get -8.

$$56x=-8x^{-3}f$$

Swap sides so that all variable terms are on the left hand side.

$$-8x^{-3}f=56x$$

The equation is in standard form.

$$\left(-\frac{8}{x^{3}}\right)f=56x$$

Divide both sides by -8x^{-3}.

$$\frac{\left(-\frac{8}{x^{3}}\right)f}{-\frac{8}{x^{3}}}=\frac{56x}{-\frac{8}{x^{3}}}$$

Dividing by -8x^{-3} undoes the multiplication by -8x^{-3}.

$$f=\frac{56x}{-\frac{8}{x^{3}}}$$

Divide 56x by -8x^{-3}.

$$f=-7x^{4}$$

Variable f cannot be equal to 0.

$$f=-7x^{4}\text{, }f\neq 0$$

Solve for x (complex solution)

$$x=\sqrt{2}\times 7^{\frac{3}{4}}\left(-\frac{1}{14}+\frac{1}{14}i\right)\sqrt[4]{f}$$

$$x=\sqrt{2}\times 7^{\frac{3}{4}}\left(\frac{1}{14}+\frac{1}{14}i\right)\sqrt[4]{f}$$

$$x=\sqrt{2}\times 7^{\frac{3}{4}}\left(-\frac{1}{14}-\frac{1}{14}i\right)\sqrt[4]{f}$$

$$x=\sqrt{2}\times 7^{\frac{3}{4}}\left(\frac{1}{14}-\frac{1}{14}i\right)\sqrt[4]{f}\text{, }f\neq 0$$

Solve for x

$$x=\frac{7^{\frac{3}{4}}\sqrt[4]{-f}}{7}$$

$$x=-\frac{7^{\frac{3}{4}}\sqrt[4]{-f}}{7}\text{, }f<0$$