What is 5^-1 equal to?

What is 5^-1 equal to?

• A. 5
• B. 1/5
• C. -1/5
• D. 1

Answer: (B)

A negative exponent means take the reciprocal of the base. For any nonzero number a, a^-n equals 1/(a^n). So 5^-1 is the reciprocal of 5, which is 1/5. This rule also works for other examples, like 2^-3 = 1/8. The other numbers shown would come from different exponents: 5 would come from exponent 1, 1 would come from exponent 0, and -1/5 would be the negative reciprocal, not the result of applying the exponent -1 to 5. So the value is 1/5.

A negative exponent means take the reciprocal of the base. For any nonzero number a, a^-n equals 1/(a^n). So 5^-1 is the reciprocal of 5, which is 1/5. This rule also works for other examples, like 2^-3 = 1/8. The other numbers shown would come from different exponents: 5 would come from exponent 1, 1 would come from exponent 0, and -1/5 would be the negative reciprocal, not the result of applying the exponent -1 to 5. So the value is 1/5.