Question

What is equivalent to 3^4×9^3

3^4*(3^2)^3
3^4*3^6
None

Answer 1

Do you know what 3^4 = ?
What does9 ^ 3 = ?

Answer 2

3 x 3 x 3 x 3 = ?
(3 x 3 ) x (3 x 3) = ?
(9) x (9) = ?
This makes it easier

Answer 3

And then you can do (9 x 9 x 9) = ?
(9x9) x (9) = ?
(81) x 9 =?

Answer 4

3^4 = 81
9^3 = 729, fyi.

Answer 5

Hope that part makes sense. Just break down the numbers and group them to make it the easiest it can possibly be!

Answer 6

3^4*(3^2)^3
So, we know (3 x 3 x 3 x 3) = 81.
(3^2)= 3 x 3 = 9
NOW we do 9^3 = 729.
Looks familiar.. :) Lets move onto the next option

Answer 7

You're making it easier to understand, thank you!

Answer 8

3^4*3^6
3^4 = (3 x 3 x 3 x 3) = 81 (This is a very popular number!)
(3 x 3 x 3 x 3 x 3 x 3) = v
(3 x 3 ) x (3 x 3) x (3x3) =
9 x 9 x 9 = 729

Answer 9

Not sure if you can pick two answers, however each seem to equal out to be the same. I'm gonna make sure I didn't mess up anywhere!

Answer 10

They probably want choice A, and I'll explain why!

Answer 11

You can pick two!

Answer 12

Oh well then I would say both, from what I worked out then :) Do you agree?

Answer 13

Yes, I agree with you!

Answer 14

Choice A technically yields :
3^4*(3^2)^3
The 3^4 is just the same as the original
(3^2) = 9
Then goes 9^3, just the same as before!
However both equal the same end result of 59049

Answer 15

So I would personally pick both. :-)

Answer 16

Do you mind helping with a few more? I would be totally grateful!

Answer 17

Sure thing! Anything to help out

Answer 18

(5^3*5^2)^4

25^20
(25^5)^4
None

Answer 19

Do you know how to work it out? Or where to start?

Answer 20

5*5*5 5*5 ?

Answer 21

Yep! Within the parentheses is ((5x5x5)x(5x5)) = (5x5x5x5x5)^4
Keep going! Lets forget about that pesky 4. What is 5^5?

Answer 22

5^3=125
5^2=25

Answer 23

Multiply them together :)

Answer 24

3125?

Answer 25

Yes!
We now know what (5^3*(5^2)) equals!
It is now 3125 ^ 4.
What does that equal?

Answer 26

12500

Answer 27

Not quite! It is actually going to equal 95367431640625. Big number, I know! We are not taking 3125 x 4 rather we are doing...
3125 x 3125 x 3125 x 3125

Answer 28

I did that, but wasn't sure if that was right!

Answer 29

Now,
25^20 = ?
(25^5)^4 = ?
Well, we can simply punch in 25^20 into the calculator. That would be typing 25 too many times.
25^20 = 9094947017729282379150390625
Then lets do (25^5)^4 = ?
Well.. (25^5) = 9765625 = (9765625)^4 = 9094947017729282379150390625
Are these related to 3125^4?

Answer 30

Doesn't seem like they are the same.

Answer 31

You are correct! They are way too big compared to 95367431640625 :-)

Answer 32

So the answer would be none! Right?(:

Answer 33

that's what I would go with!

Answer 34

It was right!

Answer 35

Awesome! Do you understand how we got the answer?

Answer 36

Yes I do. You've helped so much, thank you so much!

Answer 37

You are very much welcome :)

Answer 38

I think the idea with these problems is to make you practice the rules of operations with exponents. There is no need to multiply out the powers and get enormous numbers. You need to apply the rules of exponents and see if the expressions are equal.

Answer 39

The first problem:

3^4×9^3

A. 3^4*(3^2)^3
B. 3^4*3^6
C. None

Since 9 = 3^2, then 9^3 = (3^2)^2

That means that
3^4×9^3 = 3^4×(3^2)^3, and choice A is true

Since \((a^m)^n = a^{mn}\), then (3^2)^3 = 3^(2*3) = 3^6, so

3^4×9^3 = 3^4×(3^2)^3 = 3^4×3^6, and choice B is also true.

Answer 40

The second problem:

(5^3*5^2)^4

A.25^20
B. (25^5)^4
C. None

Since 5^3 * 5^2 = 5^(3 + 2) = 5^5, then

(5^3*5^2)^4 = (5^5)^4 = 5^20, and choice A is true.

Let's work on choice B.
25 = 5^2, so (25^5)^4 = 25^20 = (5^2)^20 = 5^40
Earlier we saw the expression is equal to 5^20, so choice B is not true.