Evaluate 6a^7 / 2a^2 using coefficient and exponent rules.

• A. 3a^5
• B. 3a^7
• C. 2a^5
• D. 12a^5

Answer: (A)

When you simplify a fraction that has the same base in the variable part, you apply two simple rules at once: divide the numeric coefficients and subtract the exponents.

For the numbers: 6 divided by 2 equals 3. For the a-terms: a^7 divided by a^2 means subtract the exponents, giving a^(7−2) = a^5. Put together, you get 3a^5.

This result follows directly from the rules for dividing powers with the same base and for dividing coefficients. If you forgot to subtract the exponents, you might end up with a^7, and if you multiplied rather than divided the numeric parts, you could get a different number like 12a^5. The correct application yields 3a^5.