Question

Josh examines the expression 5^-x over 5^x, where m is greater than 0.

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

Josh is wrong.

Explanation:

5^-x / 5^x = 5^(-x-x) = 5^-2x

= 1 / 5^2x

(you subtract the exponents when dividing )

So Josh is wrong ( he would be correct if we were multiplying)

Answer 2

Josh claim is not correct.

Explanation:

Given : Josh examines the expression
`5^(-x)` over
`5^x`, where m is greater than 0.

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.

To find : Is Josh correct? Explain why or why not.

Solution :

We first solve the Josh expression,

`5^(-x)` over
`5^x`

i.e.
`(5^(-x))/(5^x)`

We know,
`(x^a)/(x^b)=x^(a-b)`

So,
`(5^(-x))/(5^x)=5^(-x-x)`

`(5^(-x))/(5^x)=5^(-2x)`

His claim is not correct.

As the correct solution is
`(5^(-x))/(5^x)=5^(-2x)`