Basic Math Examples

$3^{3} \cdot 3 {(\frac{3}{3})}^{3} \cdot 3 {(\frac{3}{3})}^{3} \cdot 33 \frac{3}{3} \cdot 33$

Step 1

Convert $33 \frac{3}{3}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$3^{3} \cdot (3 {(\frac{3}{3})}^{3}) \cdot (3 {(\frac{3}{3})}^{3}) \cdot (33 + \frac{3}{3}) \cdot 33$

Step 1.2

Add $33$ and $\frac{3}{3}$ .

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Step 1.2.1

To write $33$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$3^{3} \cdot (3 {(\frac{3}{3})}^{3}) \cdot (3 {(\frac{3}{3})}^{3}) \cdot (33 \cdot \frac{3}{3} + \frac{3}{3}) \cdot 33$

Step 1.2.2

Combine $33$ and $\frac{3}{3}$ .

$3^{3} \cdot (3 {(\frac{3}{3})}^{3}) \cdot (3 {(\frac{3}{3})}^{3}) \cdot (\frac{33 \cdot 3}{3} + \frac{3}{3}) \cdot 33$

Step 1.2.3

Combine the numerators over the common denominator.

$3^{3} \cdot (3 {(\frac{3}{3})}^{3}) \cdot (3 {(\frac{3}{3})}^{3}) \cdot \frac{33 \cdot 3 + 3}{3} \cdot 33$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $33$ by $3$ .

$3^{3} \cdot (3 {(\frac{3}{3})}^{3}) \cdot (3 {(\frac{3}{3})}^{3}) \cdot \frac{99 + 3}{3} \cdot 33$

Step 1.2.4.2

Add $99$ and $3$ .

$3^{3} \cdot (3 {(\frac{3}{3})}^{3}) \cdot (3 {(\frac{3}{3})}^{3}) \cdot \frac{102}{3} \cdot 33$

Step 2

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

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Step 2.1

Move $3$ .

$3 \cdot 3^{3} \cdot {(\frac{3}{3})}^{3} \cdot (3 {(\frac{3}{3})}^{3}) \cdot \frac{102}{3} \cdot 33$

Step 2.2

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

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Step 2.2.1

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

$3^{1} \cdot 3^{3} \cdot {(\frac{3}{3})}^{3} \cdot (3 {(\frac{3}{3})}^{3}) \cdot \frac{102}{3} \cdot 33$

Step 2.2.2

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

$3^{1 + 3} \cdot {(\frac{3}{3})}^{3} \cdot (3 {(\frac{3}{3})}^{3}) \cdot \frac{102}{3} \cdot 33$

Step 2.3

Add $1$ and $3$ .

$3^{4} \cdot {(\frac{3}{3})}^{3} \cdot (3 {(\frac{3}{3})}^{3}) \cdot \frac{102}{3} \cdot 33$

Step 3

Multiply $3^{4}$ by $3$ by adding the exponents.

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Step 3.1

Move $3$ .

$3 \cdot 3^{4} \cdot {(\frac{3}{3})}^{3} \cdot {(\frac{3}{3})}^{3} \cdot \frac{102}{3} \cdot 33$

Step 3.2

Multiply $3$ by $3^{4}$ .

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Step 3.2.1

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

$3^{1} \cdot 3^{4} \cdot {(\frac{3}{3})}^{3} \cdot {(\frac{3}{3})}^{3} \cdot \frac{102}{3} \cdot 33$

Step 3.2.2

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

$3^{1 + 4} \cdot {(\frac{3}{3})}^{3} \cdot {(\frac{3}{3})}^{3} \cdot \frac{102}{3} \cdot 33$

Step 3.3

Add $1$ and $4$ .

$3^{5} \cdot {(\frac{3}{3})}^{3} \cdot {(\frac{3}{3})}^{3} \cdot \frac{102}{3} \cdot 33$

Step 4

Multiply ${(\frac{3}{3})}^{3}$ by ${(\frac{3}{3})}^{3}$ by adding the exponents.

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Step 4.1

Move ${(\frac{3}{3})}^{3}$ .

$3^{5} \cdot ({(\frac{3}{3})}^{3} {(\frac{3}{3})}^{3}) \cdot \frac{102}{3} \cdot 33$

Step 4.2

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

$3^{5} \cdot {(\frac{3}{3})}^{3 + 3} \cdot \frac{102}{3} \cdot 33$

Step 4.3

Add $3$ and $3$ .

$3^{5} \cdot {(\frac{3}{3})}^{6} \cdot \frac{102}{3} \cdot 33$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $3^{5} \cdot {(\frac{3}{3})}^{6}$ .

$3 (3^{4} \cdot {(\frac{3}{3})}^{6}) \cdot \frac{102}{3} \cdot 33$

Step 5.2

Cancel the common factor.

$3 (3^{4} \cdot {(\frac{3}{3})}^{6}) \cdot \frac{102}{3} \cdot 33$

Step 5.3

Rewrite the expression.

$3^{4} \cdot {(\frac{3}{3})}^{6} \cdot 102 \cdot 33$

Step 6

Simplify the expression.

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Step 6.1

Raise $3$ to the power of $4$ .

$81 \cdot {(\frac{3}{3})}^{6} \cdot 102 \cdot 33$

Step 6.2

Divide $3$ by $3$ .

$81 \cdot 1^{6} \cdot 102 \cdot 33$

Step 6.3

One to any power is one.

$81 \cdot 1 \cdot 102 \cdot 33$

Step 7

Multiply $81 \cdot 1 \cdot 102 \cdot 33$ .

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Step 7.1

Multiply $81$ by $1$ .

$81 \cdot 102 \cdot 33$

Step 7.2

Multiply $81$ by $102$ .

$8262 \cdot 33$

Step 7.3

Multiply $8262$ by $33$ .

$272646$