Basic Math Examples

${(\frac{2}{7})}^{4} {(\frac{13}{2})}^{13} {(\frac{4}{7})}^{2}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $\frac{2}{7}$ .

$\frac{2^{4}}{7^{4}} {(\frac{13}{2})}^{13} {(\frac{4}{7})}^{2}$

Step 1.2

Raise $2$ to the power of $4$ .

$\frac{16}{7^{4}} {(\frac{13}{2})}^{13} {(\frac{4}{7})}^{2}$

Step 1.3

Raise $7$ to the power of $4$ .

$\frac{16}{2401} {(\frac{13}{2})}^{13} {(\frac{4}{7})}^{2}$

Step 1.4

Apply the product rule to $\frac{13}{2}$ .

$\frac{16}{2401} \cdot \frac{13^{13}}{2^{13}} {(\frac{4}{7})}^{2}$

Step 2

Combine.

$\frac{16 \cdot 13^{13}}{2401 \cdot 2^{13}} {(\frac{4}{7})}^{2}$

Step 3

Simplify the expression.

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Step 3.1

Raise $13$ to the power of $13$ .

$\frac{16 \cdot 302875106592253}{2401 \cdot 2^{13}} {(\frac{4}{7})}^{2}$

Step 3.2

Raise $2$ to the power of $13$ .

$\frac{16 \cdot 302875106592253}{2401 \cdot 8192} {(\frac{4}{7})}^{2}$

Step 3.3

Multiply $16$ by $302875106592253$ .

$\frac{4846001705476048}{2401 \cdot 8192} {(\frac{4}{7})}^{2}$

Step 3.4

Multiply $2401$ by $8192$ .

$\frac{4846001705476048}{19668992} {(\frac{4}{7})}^{2}$

Step 4

Cancel the common factor of $4846001705476048$ and $19668992$ .

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Step 4.1

Factor $16$ out of $4846001705476048$ .

$\frac{16 (302875106592253)}{19668992} {(\frac{4}{7})}^{2}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $16$ out of $19668992$ .

$\frac{16 \cdot 302875106592253}{16 \cdot 1229312} {(\frac{4}{7})}^{2}$

Step 4.2.2

Cancel the common factor.

$\frac{16 \cdot 302875106592253}{16 \cdot 1229312} {(\frac{4}{7})}^{2}$

Step 4.2.3

Rewrite the expression.

$\frac{302875106592253}{1229312} {(\frac{4}{7})}^{2}$

Step 5

Apply the product rule to $\frac{4}{7}$ .

$\frac{302875106592253}{1229312} \cdot \frac{4^{2}}{7^{2}}$

Step 6

Combine.

$\frac{302875106592253 \cdot 4^{2}}{1229312 \cdot 7^{2}}$

Step 7

Simplify the expression.

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Step 7.1

Raise $4$ to the power of $2$ .

$\frac{302875106592253 \cdot 16}{1229312 \cdot 7^{2}}$

Step 7.2

Raise $7$ to the power of $2$ .

$\frac{302875106592253 \cdot 16}{1229312 \cdot 49}$

Step 7.3

Multiply $302875106592253$ by $16$ .

$\frac{4846001705476048}{1229312 \cdot 49}$

Step 7.4

Multiply $1229312$ by $49$ .

$\frac{4846001705476048}{60236288}$

Step 8

Cancel the common factor of $4846001705476048$ and $60236288$ .

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Step 8.1

Factor $16$ out of $4846001705476048$ .

$\frac{16 (302875106592253)}{60236288}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $16$ out of $60236288$ .

$\frac{16 \cdot 302875106592253}{16 \cdot 3764768}$

Step 8.2.2

Cancel the common factor.

$\frac{16 \cdot 302875106592253}{16 \cdot 3764768}$

Step 8.2.3

Rewrite the expression.

$\frac{302875106592253}{3764768}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{302875106592253}{3764768}$

Decimal Form:

$80449872.7656666$

Mixed Number Form:

$80449872 \frac{2882557}{3764768}$