Finite Math Examples

$\frac{x^{2}}{2^{2}} \cdot f \cdot (\frac{7}{93} + 4) + x \div \sqrt{2}$

Step 1

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

$\frac{x^{2}}{4} \cdot f \cdot (\frac{7}{93} + 4) + x \div \sqrt{2}$

Step 2

Combine $\frac{x^{2}}{4}$ and $f$ .

$\frac{x^{2} f}{4} \cdot (\frac{7}{93} + 4) + x \div \sqrt{2}$

Step 3

To write $4$ as a fraction with a common denominator, multiply by $\frac{93}{93}$ .

$\frac{x^{2} f}{4} \cdot (\frac{7}{93} + 4 \cdot \frac{93}{93}) + x \div \sqrt{2}$

Step 4

Combine $4$ and $\frac{93}{93}$ .

$\frac{x^{2} f}{4} \cdot (\frac{7}{93} + \frac{4 \cdot 93}{93}) + x \div \sqrt{2}$

Step 5

Combine the numerators over the common denominator.

$\frac{x^{2} f}{4} \cdot \frac{7 + 4 \cdot 93}{93} + x \div \sqrt{2}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $4$ by $93$ .

$\frac{x^{2} f}{4} \cdot \frac{7 + 372}{93} + x \div \sqrt{2}$

Step 6.2

Add $7$ and $372$ .

$\frac{x^{2} f}{4} \cdot \frac{379}{93} + x \div \sqrt{2}$

Step 7

Combine.

$\frac{x^{2} f \cdot 379}{4 \cdot 93} + x \div \sqrt{2}$

Step 8

Multiply $4$ by $93$ .

$\frac{x^{2} f \cdot 379}{372} + x \div \sqrt{2}$

Step 9

Move $379$ to the left of $x^{2} f$ .

$\frac{379 \cdot (x^{2} f)}{372} + x \div \sqrt{2}$

Step 10

Rewrite the division as a fraction.

$\frac{379 x^{2} f}{372} + \frac{x}{\sqrt{2}}$

Step 11

Multiply $\frac{x}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{379 x^{2} f}{372} + \frac{x}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Step 12

Combine and simplify the denominator.

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Step 12.1

Multiply $\frac{x}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{379 x^{2} f}{372} + \frac{x \sqrt{2}}{\sqrt{2} \sqrt{2}}$

Step 12.2

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{379 x^{2} f}{372} + \frac{x \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}$

Step 12.3

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{379 x^{2} f}{372} + \frac{x \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}$

Step 12.4

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

$\frac{379 x^{2} f}{372} + \frac{x \sqrt{2}}{{\sqrt{2}}^{1 + 1}}$

Step 12.5

Add $1$ and $1$ .

$\frac{379 x^{2} f}{372} + \frac{x \sqrt{2}}{{\sqrt{2}}^{2}}$

Step 12.6

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

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Step 12.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\frac{379 x^{2} f}{372} + \frac{x \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}$

Step 12.6.2

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

$\frac{379 x^{2} f}{372} + \frac{x \sqrt{2}}{2^{\frac{1}{2} \cdot 2}}$

Step 12.6.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{379 x^{2} f}{372} + \frac{x \sqrt{2}}{2^{\frac{2}{2}}}$

Step 12.6.4

Cancel the common factor of $2$ .

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Step 12.6.4.1

Cancel the common factor.

$\frac{379 x^{2} f}{372} + \frac{x \sqrt{2}}{2^{\frac{2}{2}}}$

Step 12.6.4.2

Rewrite the expression.

$\frac{379 x^{2} f}{372} + \frac{x \sqrt{2}}{2^{1}}$

Step 12.6.5

Evaluate the exponent.

$\frac{379 x^{2} f}{372} + \frac{x \sqrt{2}}{2}$