A negative exponent, such as a^(-k), is equal to what value?

A negative exponent, such as a^(-k), is equal to what value?

• A. a^k
• B. -a^k
• C. 1/a^k
• D. Undefined

Answer: (C)

A negative exponent tells you to take the reciprocal. So a^(-k) means one over a^k, provided the base a is not zero. In symbols, a^(-k) = 1/(a^k). For example, 2^(-3) = 1/8. The key idea is that the exponent rule a^m / a^n = a^(m-n) leads to a^0 = 1, so a^(-k) can be viewed as a^0 / a^k = 1/(a^k). The expression would be undefined only if the base were zero, since you can’t divide by zero. That’s why 1/a^k is the best description of a^(-k).

A negative exponent tells you to take the reciprocal. So a^(-k) means one over a^k, provided the base a is not zero. In symbols, a^(-k) = 1/(a^k). For example, 2^(-3) = 1/8.

The key idea is that the exponent rule a^m / a^n = a^(m-n) leads to a^0 = 1, so a^(-k) can be viewed as a^0 / a^k = 1/(a^k). The expression would be undefined only if the base were zero, since you can’t divide by zero.

That’s why 1/a^k is the best description of a^(-k).