In the context of mathematical exponents, which of the following statements is true?
Practice Questions
1 question
Q1
In the context of mathematical exponents, which of the following statements is true?
a^m * a^n = a^(m+n)
a^(m+n) = a^m + a^n
a^0 = 1 for any a ≠ 0
a^(-n) = 1/a^n
The correct statements regarding exponents include that a^m * a^n = a^(m+n) and a^(-n) = 1/a^n. However, a^(m+n) = a^m + a^n is incorrect.
Questions & Step-by-step Solutions
1 item
Q
Q: In the context of mathematical exponents, which of the following statements is true?
Solution: The correct statements regarding exponents include that a^m * a^n = a^(m+n) and a^(-n) = 1/a^n. However, a^(m+n) = a^m + a^n is incorrect.
Steps: 4
Step 1: Understand what exponents are. Exponents show how many times a number (the base) is multiplied by itself.
Step 2: Learn the first important rule: When you multiply two numbers with the same base, you add their exponents. This means a^m * a^n = a^(m+n).
Step 3: Learn the second important rule: A negative exponent means you take the reciprocal. So, a^(-n) = 1/a^n.
Step 4: Recognize that the statement a^(m+n) = a^m + a^n is incorrect. Exponents do not work like addition; you cannot add the results of exponents directly.
