Simplify the expression with NO negative exponents.
$\frac{3^{-4}}{5^{-2}}$

• A. ${\left(\frac{3}{5}\right)}^2$
• B. $3^4\cdot 5^2$
• C. $\frac{3^4}{5^2}$
• D. $\(\frac{5^2}{3^4}\)$

Answer: (D)

Verified step by step guidance

1. Start with the given expression: \(\frac{3^{-4}}{5^{-2}}\).
2. Recall the property of exponents that \(a^{-n} = \frac{1}{a^n}\), which means negative exponents indicate reciprocals.
3. Apply the rule for division of exponents with the same base: \(\frac{a^m}{a^n} = a^{m-n}\), but here the bases are different, so handle numerator and denominator separately.
4. Rewrite the expression by moving the bases with negative exponents to the opposite part of the fraction to make the exponents positive: \(\frac{3^{-4}}{5^{-2}} = 3^{-4} \times 5^{2}\) or equivalently \(\frac{5^{2}}{3^{4}}\).
5. Express the final simplified form with no negative exponents as \(\frac{5^{2}}{3^{4}}\).