Rewrite the expression with NO negative exponents.
$\frac{1}{5^{-3}}$

• A. $5^3$
• B. $\frac{1}{5^3}$
• C. $\frac{1}{3^5}$
• D. $5^{-3}$

Answer: (A)

Verified step by step guidance

1. Identify the expression given: \(\frac{1}{5^{-3}}\). Notice that the denominator has a negative exponent.
2. Recall the rule for negative exponents: \(a^{-n} = \frac{1}{a^n}\), which means a negative exponent indicates the reciprocal of the base raised to the positive exponent.
3. Apply this rule to the denominator: \(5^{-3} = \frac{1}{5^3}\). So the original expression becomes \(\frac{1}{\frac{1}{5^3}}\).
4. Understand that dividing by a fraction is the same as multiplying by its reciprocal. So, \(\frac{1}{\frac{1}{5^3}} = 1 \times 5^3\).
5. Therefore, the expression with no negative exponents is simply \$5^3$.