Write the Fraction in Simplest Form (5^2*5^9)/5

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

Step 1

Multiply $5^{2}$ by $5^{9}$ by adding the exponents.

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

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

Add $2$ and $9$ .

$\frac{5^{11}}{5}$

Step 2

Cancel the common factor of $5^{11}$ and $5$ .

Factor $5$ out of $5^{11}$ .

$\frac{5 \cdot 5^{10}}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$\frac{5 \cdot 5^{10}}{5 (1)}$

Cancel the common factor.

$\frac{5 \cdot 5^{10}}{5 \cdot 1}$

Rewrite the expression.

$\frac{5^{10}}{1}$

Divide $5^{10}$ by $1$ .

$5^{10}$

Step 3

Raise $5$ to the power of $10$ .

$9765625$