Simplify (225a^10)÷((5a^2)^2)

$(225 a^{10}) \div {(5 a^{2})}^{2}$

Rewrite the division as a fraction.

$\frac{225 a^{10}}{{(5 a^{2})}^{2}}$

Simplify the denominator.

Apply the product rule to $5 a^{2}$ .

$\frac{225 a^{10}}{5^{2} {(a^{2})}^{2}}$

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

$\frac{225 a^{10}}{25 {(a^{2})}^{2}}$

Multiply the exponents in ${(a^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{225 a^{10}}{25 a^{2 \cdot 2}}$

Multiply $2$ by $2$ .

$\frac{225 a^{10}}{25 a^{4}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $225$ and $25$ .

Factor $25$ out of $225 a^{10}$ .

$\frac{25 (9 a^{10})}{25 a^{4}}$

Cancel the common factors.

Factor $25$ out of $25 a^{4}$ .

$\frac{25 (9 a^{10})}{25 (a^{4})}$

Cancel the common factor.

$\frac{25 (9 a^{10})}{25 a^{4}}$

Rewrite the expression.

$\frac{9 a^{10}}{a^{4}}$

Cancel the common factor of $a^{10}$ and $a^{4}$ .

Factor $a^{4}$ out of $9 a^{10}$ .

$\frac{a^{4} (9 a^{6})}{a^{4}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{a^{4} (9 a^{6})}{a^{4} \cdot 1}$

Cancel the common factor.

$\frac{a^{4} (9 a^{6})}{a^{4} \cdot 1}$

Rewrite the expression.

$\frac{9 a^{6}}{1}$

Divide $9 a^{6}$ by $1$ .

$9 a^{6}$