Simplify the expression with NO negative exponents.
$a^3\cdot a^{-7}\cdot a^5$

• A. $a$
• B. $\frac{1}{a}$
• C. $a^{15}$
• D. $\frac{1}{a^{15}}$

Answer: (A)

Verified step by step guidance

1. Identify the expression given: \(a^{3} \cdot a^{-7} \cdot a^{5}\).
2. Recall the property of exponents that when multiplying powers with the same base, you add the exponents: \(a^{m} \cdot a^{n} = a^{m+n}\).
3. Add the exponents together: \$3 + (-7) + 5$.
4. Simplify the sum of the exponents: \$3 - 7 + 5$.
5. Rewrite the expression as a single power of \(a\) with the simplified exponent, ensuring no negative exponents remain by expressing it as a positive exponent or a fraction if needed.