How do you simplify this?

Question

[{(2^2)(2^3)}5^5]/[(2^3)(3^4)(10^5)]

How do you simplify that without having to calculate all of those things?

{ },[ ], and ( ) are all brackets by the way.

The answer is 9/16, I hope that helps!

@ pico t: I'm not quite sure what you're talking about... the brackets look fine to me.

The brackets might be a bit too confusing...

(2^2)(2^3)(5^5)
-----------------------
(2^3)(3^4)(10^5)

It's basically like that...

Sorry I'm adding so many details but I have a question... when you see that big black dot in math between two numbers, what does it mean? It appears in this question and I just thought it was a sign for multiplication but since everyone is getting different answers I thought that maybe it means something else and I'm interpreting it wrong...

9/16 is what I got in the answer key, either the answer key is wrong or I'm writing the question down wrong...

Answer 1

the brackets are just there to mess with your head:

[{(2^2)(2^3)}5^5]/[(2^3)(3^4)(10^5)]

is just:

2^2 * 2^3 * 5^5
------------------------
2^3 * 3^4 * 10^5

when it's only multiplication, the brackets don't matter so much!

now, notice that we can pair up some top & bottom stuff:

2^3
----- ... this = 1 !
2^3

that leaves us:

2^2 * 5^5
----------------
3^4 * 10^5

hmm...... notice that 10 is just 2 * 5? so we can alter another pair like this:

5^5
------- .
(2*5)^5

which is the same as

5^5
---------
2^5 * 5^5 and look... the 5^5's turn into 1, and go away, leaving

1
---
2^5

so now we have:

2^2 * 1
--------------
3^4 * 2^5

we get to do that trick with the 2's again:

2^2
-----
2^5

can reduce to just

1
--
2^3

so now we have

1 * 1
--------------
3^4 * 2^3

landing us at:

___1___
3^4 * 2^3

just have to notice the pairs of common factors, and that just takes a little practice!

Answer 2

first, let the (2^3) cancel out which leaves

{(2^2)5^5}/(3^4)10^5

which can be rewritten as {(2^2)(5^5)}/(3^4)(2X5)^5
which can be rewritten as {(2^2)(5^5)}/(3^4)(2^5)(5^5)

Now let the (5^5) cancel out which leaves

(2^2)/(3^4)(2^5). Rewrite 2^5 as (2^2)(2^3) and the equation is now

(2^2)/(3^4)(2^2)(2^3). Cancel out the (2^2) and you are left with

1/(3^4)(2^3) which equals 1/(3X3X3X3)(2X2X2), which equals 1/(81)(8) which equals 1/648. I believe your answer might be incorrect, I don't see how the answer could be 9/16...

Answer 3

{(2^2)(2^3)}5^5]/[(2^3)(3^4)(10^5)]


Well, right away you can reduce the (2^3)on top and bottom to 1 because it appears in both the numerator and the denominator. Then reduce the (5^5) on top to 1 and the (10^5) on the bottom to (5^5). Now you have (2^2)/ [(3^4)(5^5)]. Use the FOIL (first, outer, inner, last) technique in the denominator to solve.

Answer 4

(2²)(2^3)(5^5) / 2^3(3^4)(10^5)
(2^5)(5^5) / 2^3(3^4)(10^5)
10^5/2^3(3^4)(10^5)
1/2^3(3^4)
1/648

Answer 5

[{(2^2)(2^3)}5^5]/[(2^3)(3^4)(10^5)]

= [(2^2)(5^5)]/[(3^4)(10^5)]

= [(2^2)(5^5)]/[(3^4)(2^5)(5^5)]

= 1/[(3^4)(2^3)]

= 1/[81*8]

= 1/648

Answer 6

2^55^5/2^33^42^55^5=
1/(2^3*3^4)

Answer 7

( 2 ² )( 2 ³ )( 5^5 )
--------------------
( 2 ³ ) ( 3^4 ) ( 10^5 )

( 2 ² ) ( 5^5 )
---------------------
( 3^4 ) ( 2^5 ) ( 5^5 )

1
-------------
( 3^4 ) ( 2 ³ )

1
--------------
( 81 ) ( 8 )

1
----
648

Answer 8

[{(2^2)(2^3)}5^5]/[(2^3)(3^4)(10^5)]
=[(2^5)*(5^5)]/(2^3)(3^4)(10^5)
=[2^(5-3)]*(3^-4)*[(5/10)^5]
=(2^2)*(1/81)*(2^-5)
=(2^-3)*(1/81)
=(1/8)*(1/81)
=1/648
the answer you give is incorrect.

Answer 9

I am not sure why you would need an easier way to solve the question. It is pretty straight forward, just solve each exponent and solve it.