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:

$a^{-m}=\frac{1}{a^m}$

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

$5^{-1}=\frac{1}{5^1}=\frac{1}{5}$

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

Thus,

This is a value between 0 and 1.