could you please tell me how to turn this into simple radical form
2(3^(2^-1)-1)^-1
4 answers
Yelling at tutors (typing in all-capital letters) will not help. Please be patient until a math tutor comes online.
Paul has 24 sci-fi action movies, 16 comedies, and 10 dramas in his DVD collection. What percent of his DVDs are action movies?
With this kind of question, we only need to do the simplification methodically.
Start by checking all the parentheses to see if they are balanced or missing.
In the expression given, the parentheses are balanced, so that's a good start.
The -1 following the exponent operator (^) should preferably have parentheses around it to avoid confusion or ambiguity. So I am changing the expression to:
2(3^(2^-1)-1)^(-1)
If this is not the case, let me know.
From the study of exponents, we understand that x^(-1) is the same as 1/x. So we will start by removing the last exponent:
2(3^(2^-1)-1)^(-1)
=2/(3^(2^-1)-1)
The same goes for the exponent of -1 for 2, which makes
2/(3^(2^-1)-1)
=2/(3^(1/2)-1)
We have also learned that
x^(1/2) = sqrt(x), so the expression can further be reduced to:
2/(3^(1/2)-1)
=2/(sqrt(3)-1)
In general, we do not like to have expressions involving square-roots dangling in the denominator, if at all possible. This can be achived by multiplying both the numerator and denominator by the expression (sqrt(3)+1), which reduces the numerator to 2(sqrt(3)+1), and the numerator to
(sqrt(3)^2-1^2)
=3-1
=2
Cancelling the common factor 2, we should obtain the final answer as
sqrt(3)+1
Note: I have simplified the expression as I type, so I ask you to do a good job of checking my work and correct mistakes if there are any.
Start by checking all the parentheses to see if they are balanced or missing.
In the expression given, the parentheses are balanced, so that's a good start.
The -1 following the exponent operator (^) should preferably have parentheses around it to avoid confusion or ambiguity. So I am changing the expression to:
2(3^(2^-1)-1)^(-1)
If this is not the case, let me know.
From the study of exponents, we understand that x^(-1) is the same as 1/x. So we will start by removing the last exponent:
2(3^(2^-1)-1)^(-1)
=2/(3^(2^-1)-1)
The same goes for the exponent of -1 for 2, which makes
2/(3^(2^-1)-1)
=2/(3^(1/2)-1)
We have also learned that
x^(1/2) = sqrt(x), so the expression can further be reduced to:
2/(3^(1/2)-1)
=2/(sqrt(3)-1)
In general, we do not like to have expressions involving square-roots dangling in the denominator, if at all possible. This can be achived by multiplying both the numerator and denominator by the expression (sqrt(3)+1), which reduces the numerator to 2(sqrt(3)+1), and the numerator to
(sqrt(3)^2-1^2)
=3-1
=2
Cancelling the common factor 2, we should obtain the final answer as
sqrt(3)+1
Note: I have simplified the expression as I type, so I ask you to do a good job of checking my work and correct mistakes if there are any.
****
Please start a new thread for your DVD question. I prefer to know if this question came from Jen or someone else.
Please start a new thread for your DVD question. I prefer to know if this question came from Jen or someone else.
0 answers