Solve for a ((5^a)^2)/(5^3)=125

$\frac{{(5^{a})}^{2}}{5^{3}} = 125$

Multiply both sides of the equation by $5^{3}$ .

$5^{3} \frac{{(5^{a})}^{2}}{5^{3}} = 5^{3} \cdot 125$

Simplify both sides of the equation.

Simplify the left side.

Simplify $5^{3} \frac{{(5^{a})}^{2}}{5^{3}}$ .

Cancel the common factor of $5^{3}$ .

Cancel the common factor.

$5^{3} \frac{{(5^{a})}^{2}}{5^{3}} = 5^{3} \cdot 125$

Rewrite the expression.

${(5^{a})}^{2} = 5^{3} \cdot 125$

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

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

$5^{a \cdot 2} = 5^{3} \cdot 125$

Move $2$ to the left of $a$ .

$5^{2 a} = 5^{3} \cdot 125$

Simplify the right side.

Simplify $5^{3} \cdot 125$ .

Raise $5$ to the power of $3$ .

$5^{2 a} = 125 \cdot 125$

Multiply $125$ by $125$ .

$5^{2 a} = 15625$

Create equivalent expressions in the equation that all have equal bases.

$5^{2 a} = 5^{6}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 a = 6$

Divide each term in $2 a = 6$ by $2$ and simplify.

Divide each term in $2 a = 6$ by $2$ .

$\frac{2 a}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a}{2} = \frac{6}{2}$

Divide $a$ by $1$ .

$a = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$a = 3$