How do I simplify ([3^4*4^7*8^6]/3^5*4^5*8^7])^5 in a way that the result will be a fraction involving exponen

Question

In other words, rather than finding the whole number it represents, I want to simplify it (leaving it in fraction form) into the lowest numbers I can using exponents.

Answer 1

= ( (3/^4/3^5)(4^7/4^5)(8^6/8^7))^5
= ( (1/3)(4^2)(1/8))^5
=( 2/3)^5
= 32/243

Answer 2

When you have similar bases with exponents, and you are dividing, you can subtract the exponents.

So, in this case you would subtract:
4-5 = -1
7-5 = 2
6-7 = -1

You would then have:
([4^2]/[3^1 x 8^1])^5
=(16/24) ^ 5
=(4/3) ^ 5

If you want to simplify it more than that:
You could use the exponent and find the fraction.
(4^5) / (3^5)
Which is: (256/243)

Answer 3

well, when you divide exponentials that have the same base...you just subract the powers.

so for 3... 3^4/3^5 = 3^(4-5) = 3^-1
A negative exponent means 3^1 would be written in the demonator, since 3^-1 = 1/3^1

for 4...4^7/4^5 = 4^(7-5) = 4^2

for 8...8^6/8^7 = 8^-1 = 1/8^1

so...it simplifies to:
([4^2]/[3*8])^5

Now raising and exponential to a power means you multiply the exponients.

4^(2*5) = 4^10

so the final answer is:

4^10/(3^5*8^5)

Answer 4

set the full variety as a fragment because of the fact a fragment won't be able to be set as an entire variety. subsequently, the full variety is 5 so which you will set that as a fragment, you will possibly set it over a million. multiply the two fractions and additionally you gets the respond. right here, it may well be 3/4 * 5/a million = 15/4. in case you propose to make it slightly less demanding, only multiply purely the numerator by using the full variety and set that variety over the unique denominator and additionally you will possibly nonetheless get 15/4. you additionally can simplify that as a mixed variety and that is 3 3/4. wish this facilitates!

Answer 5

I get (2/3)^5... did I do something wrong? The first step should be to elimate the matching exponents, right? I get [(4^2)/(3*8)]^5, which is (16/24)^5, which is (2/3)^5, or 32/243, right?

Answer 6

thats easy. treat the exponents as numbers and rest as variables when you have same variable dividing, you subtract the exponents right?
so you have
(3^(4-5)*4^(7-5)*8^(6-7)}^5
(3^-1*4^2*8^-1)^5 or
{(4^2)/3*8}^5

if you want you can get a whole number

Answer 7

You have:

(3^4*4^7*8^6)^5
-----------------
(3^5*4^5*8^7)^5

Now, for the rule: a^n/a^m = a^n-m

So, 3^4 / 3^5 = 1/3, 4^7/4^5 = 4^2, 8^6/8^7=1/8

So you will have (1/3 * 4^2 * 1/8)^5 = (4^2/24)^5= (4*4)/(4*6)^5= (4/6)^5 = (2/3)^5

Answer 8

{3^4*4^7*8^6/ 3^5*4^5*8^7}^5=

[4^2/3*8]^5
16/24=2/3^5=32/243