Algebra Examples

$5^{2} (5^{7}) \div 5^{5}$

Step 1

Rewrite the division as a fraction.

$\frac{5^{2} (5^{7})}{5^{5}}$

Step 2

Multiply $5^{2}$ by $5^{7}$ 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.

$\frac{5^{2 + 7}}{5^{5}}$

Step 2.2

Add $2$ and $7$ .

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

Step 3

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

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Step 3.1

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

$\frac{5^{5} \cdot 5^{4}}{5^{5}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{5^{5} \cdot 5^{4}}{5^{5} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{5^{5} \cdot 5^{4}}{5^{5} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{5^{4}}{1}$

Step 3.2.4

Divide $5^{4}$ by $1$ .

$5^{4}$

Step 4

Raise $5$ to the power of $4$ .

$625$