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: \(a^{3} \cdot a^{-7} \cdot a^{5}\), which involves multiplying powers of the same base \(a\).
2. Recall the product of powers property: when multiplying expressions with the same base, add the exponents. So, combine the exponents by calculating \$3 + (-7) + 5$.
3. Perform the addition of the exponents step-by-step: first add \$3\( and \)-7\(, then add the result to \)5$.
4. Rewrite the expression as a single power of \(a\) with the exponent found in the previous step, i.e., \(a^{\text{sum of exponents}}\).
5. Since the problem requires no negative exponents, if the resulting exponent is negative, rewrite \(a^{\text{negative exponent}}\) as a fraction: \(\frac{1}{a^{\text{positive exponent}}}\).