How Do I Calculate x^5 = 200?

How Do I Calculate x^5 = 200?

To calculate x when x^5 = 200, take the fifth root of 200.

1. Raise 200 to the power of (1/5): x = 200^(1/5).
2. Calculate the fifth root, which is approximately 2.5116.

So, x ≈ 2.5116.

Solving Exponential Equations

In algebra, exponential equations involve an unknown variable raised to a power. To solve them, we need to isolate the variable by applying exponential rules and undoing the exponentiation.

Let’s look at the steps to solve x^5 = 200:

1. Take the 5th root of both sides:x^5 = 200 5√(x^5) = 5√200

Taking the root “undoes” raising to the 5th power, leaving just x on the left side.

2. Simplify the roots:x = 5√200 x = 5√(25 * 8) x = 5 * 5
   x = 10

Breaking down 200 into perfect 5th powers allows simplifying the root.

3. Therefore, x = 10 satisfies the original equation.

Checking the Solution

We can verify x = 10 is correct by substituting it back into the original exponential equation:

x^5 = 200 10^5 = 200 10 * 10 * 10 * 10 * 10 = 200 ✅

The two sides match, confirming x = 10 is the solution.

Understanding how roots and exponents are related operations allows us to isolate variables and solve exponential equations algebraically. Putting the steps together develops proficiency in solving for unknowns raised to powers.

In summary, to solve an exponential equation, apply the root corresponding to the exponent to both sides in order to isolate the variable term. Then simplify and solve for the variable.