Question

Josh examines the expression 5^-1/5^1.

He claims that the expression has a value equal to 1 because it simplifies to 5^0, and any integer to the 0 power is 1.

Is Josh correct? Explain why or why not.

Answer 1

Incorrect

Explanation:

Law of Exponent:

`\displaystyle \large{ \frac{ {a}^(m) }{ {a}^(n) } = {a}^(m - n) }`

Substitute a = 5, m = -1 and n = 1.

`\displaystyle \large{ \frac{ {5}^( - 1) }{ {5}^(1) } = {5}^( - 1 - 1) } \\ \displaystyle \large{ \frac{ {5}^( - 1) }{ {5}^(1) } = {5}^( - 2) }`

Therefore, Josh is wrong because Josh misused the law of exponent. What Josh used was a^m × a^n = a^{m+n}.