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 rule for negative exponents: \(a^{-n} = \frac{1}{a^n}\). This means that \(3^{-4} = \frac{1}{3^4}\) and \(5^{-2} = \frac{1}{5^2}\).
3. Rewrite the expression by substituting the negative exponents with their positive exponent equivalents: \(\frac{\frac{1}{3^4}}{\frac{1}{5^2}}\).
4. When dividing by a fraction, multiply by its reciprocal: \(\frac{1}{3^4} \times \frac{5^2}{1} = \frac{5^2}{3^4}\).
5. The expression is now simplified with no negative exponents: \(\frac{5^2}{3^4}\).