Basic Math Examples

${(1 - \frac{5}{3})}^{2}$

Step 1

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

${(\frac{3}{3} - \frac{5}{3})}^{2}$

Step 2

Combine the numerators over the common denominator.

${(\frac{3 - 5}{3})}^{2}$

Step 3

Subtract $5$ from $3$ .

${(\frac{- 2}{3})}^{2}$

Step 4

Move the negative in front of the fraction.

${(- \frac{2}{3})}^{2}$

Step 5

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

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Step 5.1

Apply the product rule to $- \frac{2}{3}$ .

${(- 1)}^{2} {(\frac{2}{3})}^{2}$

Step 5.2

Apply the product rule to $\frac{2}{3}$ .

${(- 1)}^{2} \frac{2^{2}}{3^{2}}$

Step 6

Raise $- 1$ to the power of $2$ .

$1 \frac{2^{2}}{3^{2}}$

Step 7

Multiply $\frac{2^{2}}{3^{2}}$ by $1$ .

$\frac{2^{2}}{3^{2}}$

Step 8

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

$\frac{4}{3^{2}}$

Step 9

Raise $3$ to the power of $2$ .

$\frac{4}{9}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{9}$

Decimal Form:

$0.\overline{4}$