Solve the following equation with a rational exponent: x^2/3=64
.(1 point)
Responses
512
512
32
32
16
16
8
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.
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
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.
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.
To solve the equation x^(2/3) = 64, you need to isolate x.
First, rewrite 64 as a power with the same base as x. Since 64 is 2^6, you can write it as x^(2/3) = (2^6).
Next, you can equate the exponents and solve for x. 2/3 * x = 6.
To solve for x, multiply both sides of the equation by 3/2 to isolate x. (2/3) * (3/2) * x = 6 * (3/2).
Simplifying, you have x = 9. Therefore, the answer is 9.
To solve the equation x^(2/3) = 64, we need to rewrite the equation in exponential form.
In exponential form, x^(2/3) = 64 can be written as (x^(1/3))^2 = 64.
Now, let's solve for x^(1/3) first.
Take the cube root of both sides to find x^(1/3):
(x^(1/3))^2 = 64
x^(1/3) = ∛64
x^(1/3) = 4
Now, cubing both sides, we get:
(x^(1/3))^3 = 4^3
x = 64
Therefore, the solution to the equation x^(2/3) = 64 is x = 64.