Simplify ((5^3)^2)/((5^2)^4)

$\frac{{(5^{3})}^{2}}{{(5^{2})}^{4}}$

Simplify the numerator.

Multiply the exponents in ${(5^{3})}^{2}$ .

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

$\frac{5^{3 \cdot 2}}{{(5^{2})}^{4}}$

Multiply $3$ by $2$ .

$\frac{5^{6}}{{(5^{2})}^{4}}$

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

$\frac{15625}{{(5^{2})}^{4}}$

Simplify the denominator.

Multiply the exponents in ${(5^{2})}^{4}$ .

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

$\frac{15625}{5^{2 \cdot 4}}$

Multiply $2$ by $4$ .

$\frac{15625}{5^{8}}$

Raise $5$ to the power of $8$ .

$\frac{15625}{390625}$

Cancel the common factor of $15625$ and $390625$ .

Factor $15625$ out of $15625$ .

$\frac{15625 (1)}{390625}$

Cancel the common factors.

Factor $15625$ out of $390625$ .

$\frac{15625 \cdot 1}{15625 \cdot 25}$

Cancel the common factor.

$\frac{15625 \cdot 1}{15625 \cdot 25}$

Rewrite the expression.

$\frac{1}{25}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{25}$

Decimal Form:

$0.04$