Question

I have a couple questions. Medals will be awarded. Ask me for the questions so I can write the equations.

Answer 1

The first equation is: \[\left(\begin{matrix}12P ^{3} \\ 15P\end{matrix}\right) \ ^{4}\]

Solve using division properties of exponents

Answer 2

That looks like a matrix to me more than anything else? What exactly is that supposed to be?

Answer 3

Is that supposed to be
\[(\frac{12P^3}{15P})^4\]?

Answer 4

You have to solve using division properties of exponents. You know like \[\frac{ 5^{6} }{ 5^{2} } = 5^{4}\]

Answer 5

Yes.

Answer 6

Okay, that makes more sense. You can approach this in at least two different ways:

1) simplify the base fraction first, then apply the exponent
2) apply the exponent first, then simplify

Which would you like to try?

Answer 7

Which ever is easier. Personally I would like to do the 1. I have a couple of questions like theese and a few word problems.

Answer 8

Okay, so what is the base fraction after you simplify it?

Answer 9

I don't know. That is the problem. Is it 0.8 or something bigger?

Answer 10

Well, let's simplify 12/15. What is that as a reduced fraction?

Answer 11

4/5?

Answer 12

Right?

Answer 13

Yes. How about P^3/P?

Answer 14

P^2? Cause you have to subtract. So is it 0.8P^2?

Answer 15

I would stick to the integers. Okay, so you have reduced the base fraction to \[\frac{4P^2}{5}\]If you raise that all to the 4th power, what do you get?

Answer 16

256P^8/625?

Answer 17

That's correct!

Answer 18

Awesome. Can I ask you some more questions?

Answer 19

Sure.

Answer 20

Alright. Next equation.

Answer 21

\[\left(\begin{matrix}3x ^{2} y ^{5} z ^{-2} \\ 5xz ^{5}\end{matrix}\right) ^{-3}\]

Answer 22

Okay, that's not an equation, technically, as there's no equals sign. It's an expression.

First thing I would do is take advantage of the fact that
\[a^{-n} =\frac{1}{a^n}\]and for a fraction, we just invert the fraction. That gives us
\[(\frac{5xz^5}{3x^2y^5z^{-2}})^3\]Next, I would simplify the base fraction...

Answer 23

What are the base fractions?

Answer 24

the base fraction is the thing inside the parentheses...that which is raised to the exponent power...

Answer 25

So raise everything in the parentheses?

Answer 26

But we are going to simplify first...

Answer 27

I don't know where to start simplifing. I don't know where to start,

Answer 28

You did it for the other one...pick the first letter, simplify that part of the fraction, move on to the next. What are the respective powers of x in numerator and denominator?

Answer 29

If you have the same letter in both numerator and denominator, you can simplify...

Answer 30

but the x is attached to variables. there is a xz^5 how do you simplify the x's

Answer 31

If you want, you can think of the fraction as

\[(\frac{5}{3}*\frac{x}{x^2}*\frac{1}{y^5}*\frac{z^5}{z^{-2}} )^3\]

Answer 32

(5/3 1/x^1 1/y^5 z^3)^3 (simplified?)

Answer 33

Close. Check your work on the z exponent.

Answer 34

oh z^7?

Answer 35

Yes.

You could write the stuff inside the parentheses (after simplification) as

\[\frac{5}{3}x^{-1}y^{-5}z^7\]which makes it easy to now apply the ^3...