Algebra Examples

$\frac{5^{6}}{5} \cdot \frac{5^{3}}{5^{2}}$

Step 1

Combine.

$\frac{5^{6} \cdot 5^{3}}{5 \cdot 5^{2}}$

Step 2

Multiply $5^{6}$ by $5^{3}$ by adding the exponents.

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Step 2.1

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

$\frac{5^{6 + 3}}{5 \cdot 5^{2}}$

Step 2.2

Add $6$ and $3$ .

$\frac{5^{9}}{5 \cdot 5^{2}}$

Step 3

Multiply $5$ by $5^{2}$ by adding the exponents.

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Step 3.1

Multiply $5$ by $5^{2}$ .

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Step 3.1.1

Raise $5$ to the power of $1$ .

$\frac{5^{9}}{5^{1} \cdot 5^{2}}$

Step 3.1.2

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

$\frac{5^{9}}{5^{1 + 2}}$

Step 3.2

Add $1$ and $2$ .

$\frac{5^{9}}{5^{3}}$

Step 4

Cancel the common factor of $5^{9}$ and $5^{3}$ .

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Step 4.1

Factor $5^{3}$ out of $5^{9}$ .

$\frac{5^{3} \cdot 5^{6}}{5^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

$\frac{5^{3} \cdot 5^{6}}{5^{3} \cdot 1}$

Step 4.2.2

Cancel the common factor.

$\frac{5^{3} \cdot 5^{6}}{5^{3} \cdot 1}$

Step 4.2.3

Rewrite the expression.

$\frac{5^{6}}{1}$

Step 4.2.4

Divide $5^{6}$ by $1$ .

$5^{6}$

Step 5

Raise $5$ to the power of $6$ .

$15625$