Question

Find the product.

(3p^4)^3 · (p^2)^7

Answer 1

This is very much like the last one we did. What would you like to do first?

Answer 2

Why don't you simplify the \((p^2)^7\) part first — what does that give you?

Answer 3

p^14

Answer 4

Yep. How about the first part?

Answer 5

I would split it apart like we did last time...

Answer 6

So... (3^4)^3... Which is 3^12?

Answer 7

Take another look, isn't it \((3p^4)^3\) ?

Answer 8

Remember, \[(ab)^n = a^nb^n\]so we can split it into \[(3)^3(p^4)^3\]

Answer 9

Oh! Okay. So... 9p^12?

Answer 10

Have to keep the exponents together with the bases they came with, no date-swapping here :-)

Getting closer...the \(p^{12}\) part is correct, but the number is incorrect.

Answer 11

\[(3)^1 = 3\]\[(3)^2 = 3*3 = 9\]\[(3)^3 = 3*3*3 = \]

Answer 12

Ohhh! Sorry. I did 3*3... Not 3*3*3. So it's 27p^12.

Answer 13

Right. Now you have to multiply \(27p^{12} p^{14}\)

Answer 14

So, 27p^26?

Answer 15

Correctamundo!

Answer 16

Got some more of these that you can use to impress me? :-)

Answer 17

Haha I'll message you some questions and answers I come up with so you can tell me if I'm getting them right :)

Answer 18

Sounds like a plan!

Answer 19

Again, Thank you! :)

Answer 20

You're welcome, of course!