Basic Math Examples

${(- \frac{13}{10})}^{2} + 2.4$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Apply the product rule to $- \frac{13}{10}$ .

${(- 1)}^{2} {(\frac{13}{10})}^{2} + 2.4$

Step 1.1.2

Apply the product rule to $\frac{13}{10}$ .

${(- 1)}^{2} \frac{13^{2}}{10^{2}} + 2.4$

Step 1.2

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

$1 \frac{13^{2}}{10^{2}} + 2.4$

Step 1.3

Multiply $\frac{13^{2}}{10^{2}}$ by $1$ .

$\frac{13^{2}}{10^{2}} + 2.4$

Step 1.4

Raise $13$ to the power of $2$ .

$\frac{169}{10^{2}} + 2.4$

Step 1.5

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

$\frac{169}{100} + 2.4$

Step 2

To write $2.4$ as a fraction with a common denominator, multiply by $\frac{100}{100}$ .

$\frac{169}{100} + 2.4 \cdot \frac{100}{100}$

Step 3

Combine $2.4$ and $\frac{100}{100}$ .

$\frac{169}{100} + \frac{2.4 \cdot 100}{100}$

Step 4

Combine the numerators over the common denominator.

$\frac{169 + 2.4 \cdot 100}{100}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2.4$ by $100$ .

$\frac{169 + 240}{100}$

Step 5.2

Add $169$ and $240$ .

$\frac{409}{100}$

Step 6

Cancel the common factor of $409$ and $100$ .

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Step 6.1

Rewrite $409$ as $1 (409)$ .

$\frac{1 (409)}{100}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Rewrite $100$ as $1 (100)$ .

$\frac{1 \cdot 409}{1 \cdot 100}$

Step 6.2.2

Cancel the common factor.

$\frac{1 \cdot 409}{1 \cdot 100}$

Step 6.2.3

Rewrite the expression.

$\frac{409}{100}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{409}{100}$

Decimal Form:

$4.09$

Mixed Number Form:

$4 \frac{9}{100}$