Simplify 5^2(5^3*5^2)

$5^{2} (5^{3} \cdot 5^{2})$

Step 1

Multiply $5^{2}$ by $5^{3}$ by adding the exponents.

Move $5^{3}$ .

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

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

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

Add $3$ and $2$ .

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

Step 2

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

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

$5^{5 + 2}$

Add $5$ and $2$ .

$5^{7}$

Step 3

Raise $5$ to the power of $7$ .

$78125$