Basic Math Examples

{(2 \frac{1}{4} \cdot 2 \frac{1}{3})}^{6}

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

Step 1

Convert

2 \frac{1}{4}

$2 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

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

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

Step 1.2

Add

2

$2$ and

\frac{1}{4}

$\frac{1}{4}$ .

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Step 1.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.2.2

Combine

2

$2$ and

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

4

$4$ .

{(\frac{8 + 1}{4} \cdot 2 \frac{1}{3})}^{6}

${(\frac{8 + 1}{4} \cdot 2 \frac{1}{3})}^{6}$

Step 1.2.4.2

Add

8

$8$ and

1

$1$ .

{(\frac{9}{4} \cdot 2 \frac{1}{3})}^{6}

${(\frac{9}{4} \cdot 2 \frac{1}{3})}^{6}$

{(\frac{9}{4} \cdot 2 \frac{1}{3})}^{6}

${(\frac{9}{4} \cdot 2 \frac{1}{3})}^{6}$

{(\frac{9}{4} \cdot 2 \frac{1}{3})}^{6}

${(\frac{9}{4} \cdot 2 \frac{1}{3})}^{6}$

{(\frac{9}{4} \cdot 2 \frac{1}{3})}^{6}

${(\frac{9}{4} \cdot 2 \frac{1}{3})}^{6}$

Step 2

Convert

2 \frac{1}{3}

$2 \frac{1}{3}$ to an improper fraction.

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Step 2.1

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

{(\frac{9}{4} \cdot (2 + \frac{1}{3}))}^{6}

${(\frac{9}{4} \cdot (2 + \frac{1}{3}))}^{6}$

Step 2.2

Add

2

$2$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 2.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

{(\frac{9}{4} \cdot (2 \cdot \frac{3}{3} + \frac{1}{3}))}^{6}

${(\frac{9}{4} \cdot (2 \cdot \frac{3}{3} + \frac{1}{3}))}^{6}$

Step 2.2.2

Combine

2

$2$ and

\frac{3}{3}

$\frac{3}{3}$ .

{(\frac{9}{4} \cdot (\frac{2 \cdot 3}{3} + \frac{1}{3}))}^{6}

${(\frac{9}{4} \cdot (\frac{2 \cdot 3}{3} + \frac{1}{3}))}^{6}$

Step 2.2.3

Combine the numerators over the common denominator.

{(\frac{9}{4} \cdot \frac{2 \cdot 3 + 1}{3})}^{6}

${(\frac{9}{4} \cdot \frac{2 \cdot 3 + 1}{3})}^{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

3

$3$ .

{(\frac{9}{4} \cdot \frac{6 + 1}{3})}^{6}

${(\frac{9}{4} \cdot \frac{6 + 1}{3})}^{6}$

Step 2.2.4.2

Add

6

$6$ and

1

$1$ .

{(\frac{9}{4} \cdot \frac{7}{3})}^{6}

${(\frac{9}{4} \cdot \frac{7}{3})}^{6}$

{(\frac{9}{4} \cdot \frac{7}{3})}^{6}

${(\frac{9}{4} \cdot \frac{7}{3})}^{6}$

{(\frac{9}{4} \cdot \frac{7}{3})}^{6}

${(\frac{9}{4} \cdot \frac{7}{3})}^{6}$

{(\frac{9}{4} \cdot \frac{7}{3})}^{6}

${(\frac{9}{4} \cdot \frac{7}{3})}^{6}$

Step 3

Cancel the common factor of

3

$3$ .

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Step 3.1

Factor

3

$3$ out of

9

$9$ .

{(\frac{3 (3)}{4} \cdot \frac{7}{3})}^{6}

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

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

Step 4

Combine

$\frac{3}{4}$ and

$7$ .

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

Step 5

Simplify the expression.

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Step 5.1

Multiply

$3$ by

$7$ .

${(\frac{21}{4})}^{6}$

Step 5.2

Apply the product rule to

$\frac{21}{4}$ .

$\frac{21^{6}}{4^{6}}$

Step 5.3

Raise

$21$ to the power of

$6$ .

$\frac{85766121}{4^{6}}$

Step 5.4

Raise

$4$ to the power of

$6$ .

$\frac{85766121}{4096}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{85766121}{4096}$

Decimal Form:

$20938.99438476 \dots$

Mixed Number Form:

$20938 \frac{4073}{4096}$