Question

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.

Part 2:

Create your own fraction with like bases, coefficients, and show its simplification.

Answer 1

I assume you know that in \( x^6\) the little 6 in the upper right means multiply x times itself 6 times?

It is short-hand, and helpful for x^20

Answer 2

$$
\cfrac{x^6}{x^2} \implies \cfrac{x^4}{1} \times\cfrac{x^2}{x^2}\\
\color{blue}{\cfrac{x^2}{x^2} = 1}\\
\cfrac{x^4}{1} \times\cfrac{x^2}{x^2} \implies \cfrac{x^4}{1} \times 1 \implies x^4
$$

Answer 3

expanded form probably means write out x times itself 6 times.

can you count to six ?

Answer 4

lol yes

Answer 5

$$\large{
\cfrac{x^6}{x^2} \implies
\cfrac{x}{1} \times\cfrac{x}{1}\times\cfrac{x}{1}\times\cfrac{x}{1}\times\cfrac{x}{x}\times\cfrac{x}{x}
}
$$

Answer 6

to simplify you need to know anything divided by itself is 1
so x/x is 1 and 1 times anything is anything (so you can ignore the 1 if you are multiplying)

Answer 7

okay so its x^4

Answer 8

it is x*x*x*x

which can also be written as \( x^4\)

Answer 9

okay thanks!