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: \(a^{3} \cdot a^{-7} \cdot a^{5}\). We are multiplying powers of the same base \(a\).
2. Recall the rule for multiplying powers with the same base: add the exponents. So, combine the exponents by calculating \$3 + (-7) + 5$.
3. Perform the addition of the exponents: \$3 + (-7) + 5$ simplifies to a single exponent value (do not calculate the final number here, just set up the addition).
4. Rewrite the expression as a single power of \(a\) with the combined exponent: \(a^{(3 + (-7) + 5)}\).
5. Since the problem asks for no negative exponents, if the resulting exponent is negative, rewrite the expression using positive exponents by applying the rule \(a^{-n} = \frac{1}{a^{n}}\).