Question

I would like to know how to simplify an equation. it's an extremely long one so i'll attach a Picture.

Answer 1

Hey Wendy :)\[\Large\rm \left(3x^{\frac{7}{2}}\right)^{6}\left(x^2\right)^{6}\]We need to apply a couple of exponent rules to simplify this down.

Answer 2

Here is one of our rules,\[\Large\rm \left(x^{\color{royalblue}{a}}\right)^{\color{orangered}{b}}=x^{\color{royalblue}{a}\color{orangered}{b}}\]When we have an exponent being applied on the outside like this, we simply multiply the numbers together.
Do you understand how we can apply this rule to the second part?\[\Large\rm \left(x^{\color{royalblue}{2}}\right)^{\color{orangered}{6}}=?\]

Answer 3

Yes, I do the second part would look like this. \[x ^{12}\]

Answer 4

\[\Large\rm \left(3x^{\frac{7}{2}}\right)^{6}\left(x^2\right)^{6}=\left(3x^{\frac{7}{2}}\right)^{6}x^{12}\]Ok nice that moves things along.

Answer 5

Another thing to keep in mind...
when we apply an exponent to a group of things,
the exponent much be applied to EACH OF THEM.

So our first bracket is actually being applied to both the 3 AND the x thing,\[\Large\rm \left(3x^{\frac{7}{2}}\right)^{6}\left(x^2\right)^{6}=3^6\left(x^{\frac{7}{2}}\right)^{6}x^{12}\]

Answer 6

The 6 is being applied to both, I meant to say*

Answer 7

I understand. So Does three get multiplied by 6? Or does three go through the normal exponent process?

Answer 8

The three doesn't get "multiplied" by the 6,
it gets an exponent of 6.

Think of it like this maybe:We again apply our exponent multiplication rule, but very carefully.
I was trying to avoid doing these two steps at once like this, but maybe we can try.