To calculate:The expression (2.7^(-11/12))/(2.7^(-1/6)) with positive exponent.

Sinead Mcgee 2020-12-13 Answered

To calculate:
The expression 2.711/122.71/6 with positive exponent.

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Expert Answer

Tasneem Almond
Answered 2020-12-14 Author has 91 answers
Formula used:
Law of exponent: For any real number a and b and rational exponents m and n for which am and an are defined, when deviding, exponents are subtracted for same base, that is,
aman=amn
Negative rational exponents:
For any non-zero number a for which am/n exist, the expression am/n means 1am/n.
Calculation:
Consider the given expression 2.711/122.71/6.
As the above expression have same base. So, use exponent law aman=amn,
2.711/122.71/6=2.711/12(1/6)
As, the denominator of exponent is same, so,
2.711/12(1/6)=2.711/12(2/6)
=2.79/12
=2.73/4
So, by reciprocating the base value of negative exponent,
2.73/4=12.73/4
Thus, the value of expression 2.711/122.71/6is12.73/4.
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To solve:
|3x+1|13.
General strategy to solve the inequalities that involve absolute value:
Absolute value inequalities deal with the inequalities (<,>,,and ) on the expressions with absolute sign.
We can use the property |x|<k is equivalent to xk and x<k, where k is a positive number and we can write a conjuction such as xk and x<k in the compact form.
k<x<k.
For example, |x|<2 and |x|>2.
|x|<2, represents the distance between x and 0 that is less than 2.
Whereas |x|>2, represents the distance between x and 0 that is greater than 2.
We can write an absolute value inequality as a compound inequality (i.e.)2<x<2.
When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.
|ax+b|<c, where c>0
=c<ax+b<c
|ax+b|>c, where c>0
=ax+b<c or ax+b>c
We can replace > above with  and < with .

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