solve the following equation with a rational exponent 2x 3/2 = 16

Answer 1

To solve the equation 2x^(3/2) = 16, we can rewrite it as:

x^(3/2) = 16/2

x^(3/2) = 8

Now, we will cube both sides of the equation to eliminate the rational exponent of 3/2:

(x^(3/2))^3 = 8^3

x^(9/2) = 512

Now, we can rewrite the equation with a rational exponent as:

x^(9/2) - 512 = 0

To solve this equation, we can raise both sides of the equation to the power of 2/9:

(x^(9/2))^(2/9) - 512^(2/9) = 0^(2/9)

x^(9/2 * 2/9) - 512^(2/9) = 0

x^(1/1) - 2 = 0

x - 2 = 0

x = 2

Therefore, the solution to the equation 2x^(3/2) = 16 is x = 2.

Answer 2

solve the following equation with a rational exponent: 5x 4/3 = 80

Answer 3

To solve the equation 5x^(4/3) = 80, we can rewrite it as:

x^(4/3) = 80/5

x^(4/3) = 16

Now, we will raise both sides of the equation to the power of 3/4 to eliminate the rational exponent of 4/3:

(x^(4/3))^(3/4) = 16^(3/4)

x^(4/3 * 3/4) = 16^(3/4)

x^(1/1) = 16^(3/4)

x = 16^(3/4)

To simplify 16^(3/4), we can rewrite it as (2^4)^(3/4) since 16 is 2 raised to the power of 4:

x = (2^4)^(3/4)

x = 2^(4 * 3/4)

x = 2^3

x = 8

Therefore, the solution to the equation 5x^(4/3) = 80 is x = 8.

Answer 4

solve the following equation with a rational exponent x 2/3 = 64

Answer 5

To solve the equation x^(2/3) = 64, we can rewrite it as:

x = 64^(3/2)

To simplify 64^(3/2), we can rewrite it as (8^2)^(3/2) since 64 is 8 raised to the power of 2:

x = (8^2)^(3/2)

x = 8^(2 * 3/2)

x = 8^3

x = 512

Therefore, the solution to the equation x^(2/3) = 64 is x = 512.