Calculus Examples

$\frac{1}{n^{\frac{1}{2}}} \cdot \frac{1}{n} = x$

Step 1

Rewrite the equation as $x = \frac{1}{n^{\frac{1}{2}}} \cdot \frac{1}{n}$ .

$x = \frac{1}{n^{\frac{1}{2}}} \cdot \frac{1}{n}$

Step 2

Simplify $\frac{1}{n^{\frac{1}{2}}} \cdot \frac{1}{n}$ .

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Step 2.1

Combine.

$x = \frac{1 \cdot 1}{n^{\frac{1}{2}} n}$

Step 2.2

Multiply $n^{\frac{1}{2}}$ by $n$ by adding the exponents.

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Step 2.2.1

Multiply $n^{\frac{1}{2}}$ by $n$ .

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Step 2.2.1.1

Raise $n$ to the power of $1$ .

$x = \frac{1 \cdot 1}{n^{\frac{1}{2}} n^{1}}$

Step 2.2.1.2

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

$x = \frac{1 \cdot 1}{n^{\frac{1}{2} + 1}}$

Step 2.2.2

Write $1$ as a fraction with a common denominator.

$x = \frac{1 \cdot 1}{n^{\frac{1}{2} + \frac{2}{2}}}$

Step 2.2.3

Combine the numerators over the common denominator.

$x = \frac{1 \cdot 1}{n^{\frac{1 + 2}{2}}}$

Step 2.2.4

Add $1$ and $2$ .

$x = \frac{1 \cdot 1}{n^{\frac{3}{2}}}$

Step 2.3

Multiply $1$ by $1$ .

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