If you multiply two powers with the same base, a^n * a^m, the exponents are:

If you multiply two powers with the same base, a^n * a^m, the exponents are:

• A. a^(n-m)
• B. a^n * a^m
• C. a^(n+m)
• D. a^(m-n)

Answer: (C)

When you multiply two powers with the same base, you add the exponents. So a^n times a^m equals a^(n+m). This happens because you're combining how many times you multiply the base by itself. For example, 2^3 times 2^5 is 2^(3+5) = 2^8, which is 256. The idea works for any base a and any exponents n and m. The other forms would come from different operations: a^(n-m) would come from dividing powers or subtracting exponents, and a^(m-n) is just the same subtraction with the order swapped. Thus the correct expression is a^(n+m).

When you multiply two powers with the same base, you add the exponents. So a^n times a^m equals a^(n+m). This happens because you're combining how many times you multiply the base by itself. For example, 2^3 times 2^5 is 2^(3+5) = 2^8, which is 256. The idea works for any base a and any exponents n and m. The other forms would come from different operations: a^(n-m) would come from dividing powers or subtracting exponents, and a^(m-n) is just the same subtraction with the order swapped. Thus the correct expression is a^(n+m).