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.
solve the following equation with a rational exponent 2x 3/2 = 16
5 answers
solve the following equation with a rational exponent: 5x 4/3 = 80
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.
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.
solve the following equation with a rational exponent x 2/3 = 64
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.
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.