Question

Please help I have no clue what to do and my grades go in tomorrow morning at 9:00

Answer 1

A)

Part 1:

We can use the exponential rule shown below:

`a^m\cdot a^n=a^(m+n)`

when same bases are multiplied, the exponents are added

Thus,

`\begin{gathered} 5^3\cdot5^(-4) \\ =5^(3-4) \\ =5^(-1) \end{gathered}`

Part 2:

We can use another exponents rule:

`a^(-m)=(1)/(a^m)`

Now, we can write 5^ -1 in another form:

`5^(-1)=(1)/(5^1)=(1)/(5)`

One fifth is a fraction that is definitely above 0 and less than 1.

Thus,

This is a value between 0 and 1.