Question

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

Answer 1

Answer:

Josh claim is not correct.

Step-by-step 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. $\frac{5^{-x}}{5^x}$

We know, $\frac{x^a}{x^b}=x^{a-b}$

So, $\frac{5^{-x}}{5^x}=5^{-x-x}$

$\frac{5^{-x}}{5^x}=5^{-2x}$

His claim is not correct.

As the correct solution is $\frac{5^{-x}}{5^x}=5^{-2x}$

Answer 2

Answer:

Josh is wrong.

Step-by-step 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)