Solve for c (5^6)/(5^2)=5^c

$\frac{5^{6}}{5^{2}} = 5^{c}$

Rewrite the equation as $5^{c} = \frac{5^{6}}{5^{2}}$ .

$5^{c} = \frac{5^{6}}{5^{2}}$

Move $5^{2}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$5^{c} = 5^{6} \cdot 5^{- 2}$

Multiply $5^{6}$ by $5^{- 2}$ by adding the exponents.

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

$5^{c} = 5^{6 - 2}$

Subtract $2$ from $6$ .

$5^{c} = 5^{4}$

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

$c = 4$