# Evaluate the following?

##### 5 Answers

#### Explanation:

Using the rules of exponents that

#=(7^6)^(1/6)/(11^6)^(1/6)#

#=7^(6*1/6)/11^(6*1/6)#

#=7^1/11^1#

#=7/11#

#### Explanation:

This is exactly the same concept as a previous question with an index of

=

#### Explanation:

Check

- Last digit is odd, so not divisible by
#2# . - Sum of digits is
#1+1+7+6+4+9 = 28# not divisible by#3# . - Last digit is not
#0# or#5# , so not divisible by#5# #117649/7 = 16807# , so divisible by#7# #16807/7 = 2401# #2401/7 = 343# #343/7 = 49# #49/7 = 7#

So

So if the answer is exact, we require the denominator to be a perfect

Let's do some approximating...

#1771561/117649 ~~ 177/12 ~~ 14#

#sqrt(14) ~~ 4#

#root(3)(4) ~~ 3/2#

So:

#3/2*7 ~~ 11#

Try:

#1771561/11 = 161051# #161051/11 = 14641# #14641/11 = 1331# #1331/11 = 121# #121/11 = 11#

So

Hence:

#(117649/1771561)^(1/6) = (7^6/11^6)^(1/6) = 7/11#

#### Explanation:

Computing the rational number with fractional exponent

example of:

The rational number above

Prime Factorization :

Then we apply the power of a power with base

Calculator reveals the value as

0.6363636363..