Solve for f d=16ef^2

$d = 16 e f^{2}$

Step 1

Rewrite the equation as $16 e f^{2} = d$ .

$16 e f^{2} = d$

Step 2

Divide each term in $16 e f^{2} = d$ by $16 e$ and simplify.

Divide each term in $16 e f^{2} = d$ by $16 e$ .

$\frac{16 e f^{2}}{16 e} = \frac{d}{16 e}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 e f^{2}}{16 e} = \frac{d}{16 e}$

Rewrite the expression.

$\frac{e f^{2}}{e} = \frac{d}{16 e}$

Cancel the common factor of $e$ .

Cancel the common factor.

$\frac{e f^{2}}{e} = \frac{d}{16 e}$

Divide $f^{2}$ by $1$ .

$f^{2} = \frac{d}{16 e}$

Step 3

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$f = \pm \sqrt{\frac{d}{16 e}}$

Step 4

Simplify $\pm \sqrt{\frac{d}{16 e}}$ .

Rewrite $\frac{d}{16 e}$ as ${(\frac{1}{2^{2}})}^{2} \frac{d}{e}$ .

Factor the perfect power $1^{2}$ out of $d$ .

$f = \pm \sqrt{\frac{1^{2} d}{16 e}}$

Factor the perfect power ${(2^{2})}^{2}$ out of $16 e$ .

$f = \pm \sqrt{\frac{1^{2} d}{{(2^{2})}^{2} e}}$

Rearrange the fraction $\frac{1^{2} d}{{(2^{2})}^{2} e}$ .

$f = \pm \sqrt{{(\frac{1}{2^{2}})}^{2} \frac{d}{e}}$

Pull terms out from under the radical.

$f = \pm \frac{1}{2^{2}} \sqrt{\frac{d}{e}}$

Raise $2$ to the power of $2$ .

$f = \pm \frac{1}{4} \sqrt{\frac{d}{e}}$

Rewrite $\sqrt{\frac{d}{e}}$ as $\frac{\sqrt{d}}{\sqrt{e}}$ .

$f = \pm \frac{1}{4} \cdot \frac{\sqrt{d}}{\sqrt{e}}$

Multiply $\frac{\sqrt{d}}{\sqrt{e}}$ by $\frac{\sqrt{e}}{\sqrt{e}}$ .

$f = \pm \frac{1}{4} (\frac{\sqrt{d}}{\sqrt{e}} \cdot \frac{\sqrt{e}}{\sqrt{e}})$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{d}}{\sqrt{e}}$ by $\frac{\sqrt{e}}{\sqrt{e}}$ .

$f = \pm \frac{1}{4} \cdot \frac{\sqrt{d} \sqrt{e}}{\sqrt{e} \sqrt{e}}$

Raise $\sqrt{e}$ to the power of $1$ .

$f = \pm \frac{1}{4} \cdot \frac{\sqrt{d} \sqrt{e}}{{\sqrt{e}}^{1} \sqrt{e}}$

Raise $\sqrt{e}$ to the power of $1$ .

$f = \pm \frac{1}{4} \cdot \frac{\sqrt{d} \sqrt{e}}{{\sqrt{e}}^{1} {\sqrt{e}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f = \pm \frac{1}{4} \cdot \frac{\sqrt{d} \sqrt{e}}{{\sqrt{e}}^{1 + 1}}$

Add $1$ and $1$ .

$f = \pm \frac{1}{4} \cdot \frac{\sqrt{d} \sqrt{e}}{{\sqrt{e}}^{2}}$

Rewrite ${\sqrt{e}}^{2}$ as $e$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{e}$ as $e^{\frac{1}{2}}$ .

$f = \pm \frac{1}{4} \cdot \frac{\sqrt{d} \sqrt{e}}{{(e^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$f = \pm \frac{1}{4} \cdot \frac{\sqrt{d} \sqrt{e}}{e^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$f = \pm \frac{1}{4} \cdot \frac{\sqrt{d} \sqrt{e}}{e^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$f = \pm \frac{1}{4} \cdot \frac{\sqrt{d} \sqrt{e}}{e^{\frac{2}{2}}}$

Rewrite the expression.

$f = \pm \frac{1}{4} \cdot \frac{\sqrt{d} \sqrt{e}}{e^{1}}$

Simplify.

$f = \pm \frac{1}{4} \cdot \frac{\sqrt{d} \sqrt{e}}{e}$

Combine using the product rule for radicals.

$f = \pm \frac{1}{4} \cdot \frac{\sqrt{d e}}{e}$

Multiply $\frac{1}{4}$ by $\frac{\sqrt{d e}}{e}$ .

$f = \pm \frac{\sqrt{d e}}{4 e}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$f = \frac{\sqrt{d e}}{4 e}$

Next, use the negative value of the $\pm$ to find the second solution.

$f = - \frac{\sqrt{d e}}{4 e}$

The complete solution is the result of both the positive and negative portions of the solution.

$f = \frac{\sqrt{d e}}{4 e}$

$f = - \frac{\sqrt{d e}}{4 e}$

$f = \frac{\sqrt{d e}}{4 e}$

$f = - \frac{\sqrt{d e}}{4 e}$

Solve for f d=16ef^2

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