Question

Can someone explain to me how I can solve this?

Show the expanded form and simplification of x to the 6th power over x to the second power. Explain in your own words how you can simplify x to the 6th power over x to the second power without having to write the expanded form.

Answer 1

x to the n power divided by (or over) x to a m power equals x to the (n - m) power.

So in this case, x to the 6th power over x to the second power equals x to the (6th - 2nd) power =
x to the (6 - 2) which equals x to the 4th power

So the answer is x to the fourth power

Answer 2

Oops...that should have been:
\[\frac{x^6}{x^2}=\frac{x*x*x*x*x*x}{x*x}\]

Answer 3

You do know that
\[ \frac{x}{x} =1 \]
and you can write the problem as
\[ \frac{x}{x}\cdot \frac{x}{x} \cdot \frac{x\cdot x \cdot x\cdot x}{1} \]
if you simplify (make the x/x 1), then count the number of x's left