Question

Solve the following equation with a rational exponent: x^2/3=64
.(1 point)
Responses

512
512

32
32

16
16

8

Answer 1

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

Answer 2

not cool to just repeat my solution, pretending it's your own

Answer 3

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.

Answer 4

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.

Answer 5

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.