To solve the equation, we need to eliminate the rational exponent. We can do this by raising both sides of the equation to the reciprocal of the exponent.
x^(2/3) = 64^(1/3)
Raising both sides to the reciprocal of 2/3 (which is 3/2), we get:
(x^(2/3))^(3/2) = (64^(1/3))^(3/2)
Simplifying, we have:
x^(2/3 * 3/2) = 64^(1/3 * 3/2)
x^(1) = 64^(1/2)
x = 64^(1/2)
Taking the square root of 64, we have:
x = √64
x = 8
So, the solution to the equation x^(2/3) = 64 is x = 8.
Solve the following equation with a rational exponent: x^2/3=64
.(1 point)
Responses
512
512
32
32
16
16
8
5 answers
This question is much too hard for the bot, needs
human intervention: .....
x^2/3=64
(x^2/3)^(3/2)=64^(3/2)
x = 8^3 = 512
human intervention: .....
x^2/3=64
(x^2/3)^(3/2)=64^(3/2)
x = 8^3 = 512
Apologies for the incorrect response earlier. You are correct. Let's solve the equation correctly.
To solve the equation x^(2/3) = 64, we need to eliminate the rational exponent by raising both sides of the equation to the reciprocal of the exponent.
(x^(2/3))^(3/2) = 64^(3/2)
Simplifying, we have:
x^(2/3 * 3/2) = 64^(3/2)
x^1 = 64^(3/2)
x = 64^(3/2)
Finding the square root of 64 and then cubing the result, we have:
x = √64^3 = 8^3 = 512
So, the solution to the equation x^(2/3) = 64 is x = 512.
To solve the equation x^(2/3) = 64, we need to eliminate the rational exponent by raising both sides of the equation to the reciprocal of the exponent.
(x^(2/3))^(3/2) = 64^(3/2)
Simplifying, we have:
x^(2/3 * 3/2) = 64^(3/2)
x^1 = 64^(3/2)
x = 64^(3/2)
Finding the square root of 64 and then cubing the result, we have:
x = √64^3 = 8^3 = 512
So, the solution to the equation x^(2/3) = 64 is x = 512.
not cool to just repeat my solution, pretending it's your own
Apologies for the oversight. Thank you for pointing it out. I appreciate your solution, and you are correct that x = 512 is the correct solution to the equation x^(2/3) = 64. Thank you for providing the correct solution.
1 answer