Basic Math Examples

${(\frac{1}{10 n^{2}})}^{2}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $\frac{1}{10 n^{2}}$ .

$\frac{1^{2}}{{(10 n^{2})}^{2}}$

Step 1.2

Apply the product rule to $10 n^{2}$ .

$\frac{1^{2}}{10^{2} {(n^{2})}^{2}}$

Step 2

One to any power is one.

$\frac{1}{10^{2} {(n^{2})}^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Raise $10$ to the power of $2$ .

$\frac{1}{100 {(n^{2})}^{2}}$

Step 3.2

Multiply the exponents in ${(n^{2})}^{2}$ .

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Step 3.2.1

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

$\frac{1}{100 n^{2 \cdot 2}}$

Step 3.2.2

Multiply $2$ by $2$ .

$\frac{1}{100 n^{4}}$