Basic Math Examples

$\frac{2 \cdot 3^{2} + 5 \cdot 3 + 6}{3 \cdot 3^{2} - 7 \cdot 3 + 2}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{2 \cdot 9 + 5 \cdot 3 + 6}{3 \cdot 3^{2} - 7 \cdot 3 + 2}$

Step 1.2

Multiply $2$ by $9$ .

$\frac{18 + 5 \cdot 3 + 6}{3 \cdot 3^{2} - 7 \cdot 3 + 2}$

Step 1.3

Multiply $5$ by $3$ .

$\frac{18 + 15 + 6}{3 \cdot 3^{2} - 7 \cdot 3 + 2}$

Step 1.4

Add $18$ and $15$ .

$\frac{33 + 6}{3 \cdot 3^{2} - 7 \cdot 3 + 2}$

Step 1.5

Add $33$ and $6$ .

$\frac{39}{3 \cdot 3^{2} - 7 \cdot 3 + 2}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $3$ by $3^{2}$ by adding the exponents.

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Step 2.1.1

Multiply $3$ by $3^{2}$ .

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Step 2.1.1.1

Raise $3$ to the power of $1$ .

$\frac{39}{3^{1} \cdot 3^{2} - 7 \cdot 3 + 2}$

Step 2.1.1.2

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

$\frac{39}{3^{1 + 2} - 7 \cdot 3 + 2}$

Step 2.1.2

Add $1$ and $2$ .

$\frac{39}{3^{3} - 7 \cdot 3 + 2}$

Step 2.2

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

$\frac{39}{27 - 7 \cdot 3 + 2}$

Step 2.3

Multiply $- 7$ by $3$ .

$\frac{39}{27 - 21 + 2}$

Step 2.4

Subtract $21$ from $27$ .

$\frac{39}{6 + 2}$

Step 2.5

Add $6$ and $2$ .

$\frac{39}{8}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{39}{8}$

Decimal Form:

$4.875$

Mixed Number Form:

$4 \frac{7}{8}$