Algebra Examples

$\frac{3^{8} + 3^{5}}{3^{5} + 9^{2}} \cdot \frac{5^{2} - 5^{5}}{5^{5} + 5^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $3$ to the power of $8$ .

$\frac{6561 + 3^{5}}{3^{5} + 9^{2}} \cdot \frac{5^{2} - 5^{5}}{5^{5} + 5^{2}}$

Step 1.2

Raise $3$ to the power of $5$ .

$\frac{6561 + 243}{3^{5} + 9^{2}} \cdot \frac{5^{2} - 5^{5}}{5^{5} + 5^{2}}$

Step 1.3

Add $6561$ and $243$ .

$\frac{6804}{3^{5} + 9^{2}} \cdot \frac{5^{2} - 5^{5}}{5^{5} + 5^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Raise $3$ to the power of $5$ .

$\frac{6804}{243 + 9^{2}} \cdot \frac{5^{2} - 5^{5}}{5^{5} + 5^{2}}$

Step 2.2

Raise $9$ to the power of $2$ .

$\frac{6804}{243 + 81} \cdot \frac{5^{2} - 5^{5}}{5^{5} + 5^{2}}$

Step 2.3

Add $243$ and $81$ .

$\frac{6804}{324} \cdot \frac{5^{2} - 5^{5}}{5^{5} + 5^{2}}$

Step 3

Simplify the numerator.

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Step 3.1

Raise $5$ to the power of $2$ .

$\frac{6804}{324} \cdot \frac{25 - 5^{5}}{5^{5} + 5^{2}}$

Step 3.2

Raise $5$ to the power of $5$ .

$\frac{6804}{324} \cdot \frac{25 - 1 \cdot 3125}{5^{5} + 5^{2}}$

Step 3.3

Multiply $- 1$ by $3125$ .

$\frac{6804}{324} \cdot \frac{25 - 3125}{5^{5} + 5^{2}}$

Step 3.4

Subtract $3125$ from $25$ .

$\frac{6804}{324} \cdot \frac{- 3100}{5^{5} + 5^{2}}$

Step 4

Simplify the denominator.

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Step 4.1

Raise $5$ to the power of $5$ .

$\frac{6804}{324} \cdot \frac{- 3100}{3125 + 5^{2}}$

Step 4.2

Raise $5$ to the power of $2$ .

$\frac{6804}{324} \cdot \frac{- 3100}{3125 + 25}$

Step 4.3

Add $3125$ and $25$ .

$\frac{6804}{324} \cdot \frac{- 3100}{3150}$

Step 5

Simplify terms.

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Step 5.1

Cancel the common factor of $126$ .

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Step 5.1.1

Factor $126$ out of $6804$ .

$\frac{126 (54)}{324} \cdot \frac{- 3100}{3150}$

Step 5.1.2

Factor $126$ out of $3150$ .

$\frac{126 \cdot 54}{324} \cdot \frac{- 3100}{126 \cdot 25}$

Step 5.1.3

Cancel the common factor.

$\frac{126 \cdot 54}{324} \cdot \frac{- 3100}{126 \cdot 25}$

Step 5.1.4

Rewrite the expression.

$\frac{54}{324} \cdot \frac{- 3100}{25}$

Step 5.2

Cancel the common factor of $4$ .

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Step 5.2.1

Factor $4$ out of $324$ .

$\frac{54}{4 (81)} \cdot \frac{- 3100}{25}$

Step 5.2.2

Factor $4$ out of $- 3100$ .

$\frac{54}{4 \cdot 81} \cdot \frac{4 \cdot - 775}{25}$

Step 5.2.3

Cancel the common factor.

$\frac{54}{4 \cdot 81} \cdot \frac{4 \cdot - 775}{25}$

Step 5.2.4

Rewrite the expression.

$\frac{54}{81} \cdot \frac{- 775}{25}$

Step 5.3

Multiply $\frac{54}{81}$ by $\frac{- 775}{25}$ .

$\frac{54 \cdot - 775}{81 \cdot 25}$

Step 5.4

Multiply.

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Step 5.4.1

Multiply $54$ by $- 775$ .

$\frac{- 41850}{81 \cdot 25}$

Step 5.4.2

Multiply $81$ by $25$ .

$\frac{- 41850}{2025}$

Step 5.5

Cancel the common factor of $- 41850$ and $2025$ .

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Step 5.5.1

Factor $675$ out of $- 41850$ .

$\frac{675 (- 62)}{2025}$

Step 5.5.2

Cancel the common factors.

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Step 5.5.2.1

Factor $675$ out of $2025$ .

$\frac{675 \cdot - 62}{675 \cdot 3}$

Step 5.5.2.2

Cancel the common factor.

$\frac{675 \cdot - 62}{675 \cdot 3}$

Step 5.5.2.3

Rewrite the expression.

$\frac{- 62}{3}$

Step 5.6

Move the negative in front of the fraction.

$- \frac{62}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{62}{3}$

Decimal Form:

$- 20.\overline{6}$

Mixed Number Form:

$- 20 \frac{2}{3}$