Finite Math Examples

${(\frac{5}{9 i})}^{2}$

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 $\frac{5}{9 i}$ .

$\frac{5^{2}}{{(9 i)}^{2}}$

Step 1.2

Apply the product rule to $9 i$ .

$\frac{5^{2}}{9^{2} i^{2}}$

Step 2

Raise $5$ to the power of $2$ .

$\frac{25}{9^{2} i^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Raise $9$ to the power of $2$ .

$\frac{25}{81 i^{2}}$

Step 3.2

Rewrite $i^{2}$ as $- 1$ .

$\frac{25}{81 \cdot - 1}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $81$ by $- 1$ .

$\frac{25}{- 81}$

Step 4.2

Move the negative in front of the fraction.

$- \frac{25}{81}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{25}{81}$

Decimal Form:

$- 0.30864197 \dots$