Algebra Examples

$3^{2} + (7 - 2) \cdot 4 - \frac{6}{3}$

Step 1

Find the common denominator.

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Step 1.1

Write $3^{2}$ as a fraction with denominator $1$ .

$\frac{3^{2}}{1} + (7 - 2) \cdot 4 - \frac{6}{3}$

Step 1.2

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

$\frac{3^{2}}{1} \cdot \frac{3}{3} + (7 - 2) \cdot 4 - \frac{6}{3}$

Step 1.3

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

$\frac{3^{2} \cdot 3}{3} + (7 - 2) \cdot 4 - \frac{6}{3}$

Step 1.4

Write $(7 - 2) \cdot 4$ as a fraction with denominator $1$ .

$\frac{3^{2} \cdot 3}{3} + \frac{(7 - 2) \cdot 4}{1} - \frac{6}{3}$

Step 1.5

Multiply $\frac{(7 - 2) \cdot 4}{1}$ by $\frac{3}{3}$ .

$\frac{3^{2} \cdot 3}{3} + \frac{(7 - 2) \cdot 4}{1} \cdot \frac{3}{3} - \frac{6}{3}$

Step 1.6

Multiply $\frac{(7 - 2) \cdot 4}{1}$ by $\frac{3}{3}$ .

$\frac{3^{2} \cdot 3}{3} + \frac{(7 - 2) \cdot 4 \cdot 3}{3} - \frac{6}{3}$

Step 2

Combine the numerators over the common denominator.

$\frac{3^{2} \cdot 3 + (7 - 2) \cdot 4 \cdot 3 - 6}{3}$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

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

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Step 3.1.1.1

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

$\frac{3^{2} \cdot 3^{1} + (7 - 2) \cdot 4 \cdot 3 - 6}{3}$

Step 3.1.1.2

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

$\frac{3^{2 + 1} + (7 - 2) \cdot 4 \cdot 3 - 6}{3}$

Step 3.1.2

Add $2$ and $1$ .

$\frac{3^{3} + (7 - 2) \cdot 4 \cdot 3 - 6}{3}$

Step 3.2

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

$\frac{27 + (7 - 2) \cdot 4 \cdot 3 - 6}{3}$

Step 3.3

Subtract $2$ from $7$ .

$\frac{27 + 5 \cdot 4 \cdot 3 - 6}{3}$

Step 3.4

Multiply $5 \cdot 4 \cdot 3$ .

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Step 3.4.1

Multiply $5$ by $4$ .

$\frac{27 + 20 \cdot 3 - 6}{3}$

Step 3.4.2

Multiply $20$ by $3$ .

$\frac{27 + 60 - 6}{3}$

Step 4

Simplify the expression.

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Step 4.1

Add $27$ and $60$ .

$\frac{87 - 6}{3}$

Step 4.2

Subtract $6$ from $87$ .

$\frac{81}{3}$

Step 4.3

Divide $81$ by $3$ .

$27$