lol apparently Jen also had the same question
2(3^(2^-1)-1)^-1
I do not understand how to do this one either
See answer to Jen's first question.
2(3^(2^-1)-1)^-1
work you way out from the inside
= 2(3^(1/2)-1)^-1
= 2(√3 -1 )^-1
= 2/(√3 - 1)
= 2/(√3 - 1)*(√3 + 1)/(√3 + 1)
= 2(√3 + 1)(3-1)
= √3 + 1
or 2.732...
or http://www.google.ca/search?hl=en&q=2(3^(2^-1)-1)^-1+&btnG=Google+Search&aq=f&oq=
Didn't realize that MathMate already answered the same question for Jen
Good to know that we got the same answer and Google also concurred
No problem! Let's break down the expression step by step.
First, let's simplify the inner part of the expression:
3^(2^-1)
To simplify this, let's focus on the exponent first. The exponent in this case is 2^-1. To evaluate a negative exponent, we can rewrite it as the reciprocal of the positive exponent:
2^-1 = 1/(2^1) = 1/2
Now, we can substitute the simplified exponent back into the expression:
3^(2^-1) = 3^(1/2)
Now, let's simplify the outer part of the expression:
(3^(1/2) - 1)^-1
This is a subtraction inside a set of parentheses, so we need to evaluate that subtraction first.
3^(1/2) - 1
To simplify this, we need to calculate the square root of 3 and then subtract 1.
Using a calculator, we can find that the square root of 3 is approximately 1.732.
Now we can substitute the values back into the expression and simplify further:
(1.732 - 1)^-1 = 0.732^-1
To find the reciprocal of a number, we simply flip it:
0.732^-1 = 1/0.732
Finally, let's substitute the simplified value of the inner expression back into the original expression:
2(1/0.732) = 2/0.732
To simplify this further, we can rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator. In this case, the conjugate of 0.732 is also 0.732.
(2/0.732) * (0.732/0.732) = 1.366
Therefore, the simplified value of the expression 2(3^(2^-1)-1)^-1 is approximately 1.366.