What is the value of x when x8=200 ?(1 point) Responses 208 208 25 25 1600 1600 192
The value of x when x * 8 = 200 is 25.
To find the value of x, we need to isolate x in the equation x * 8 = 200. To do this, we divide both sides of the equation by 8.
x * 8 / 8 = 200 / 8
This simplifies to:
x = 25
Therefore, the value of x when x * 8 is equal to 200 is 25.
To find the value of x, we need to solve the equation x^8 = 200. Here's how you can do it:
1. Start by taking the eighth root of both sides of the equation. This cancels out the exponent of 8.
∛(x^8) = ∛200
2. Simplify the left side by using the properties of exponents:
x^(8/3) = ∛200
3. Take the cube root (∛) of 200 using a calculator or by hand:
∛200 ≈ 5.848
4. Now, raise both sides of the equation to the power of 3/8, using the reciprocal of the exponent 8/3:
(x^(8/3))^(3/8) = (5.848)^(3/8)
5. Simplify the left side by using the property of exponents:
x = (5.848)^(3/8)
6. Calculate the right side of the equation using a calculator:
(5.848)^(3/8) ≈ 2.232
Therefore, the value of x when x^8 = 200 is approximately 2.232.