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(x+6)^3/5=8

2 min read Jun 17, 2024
(x+6)^3/5=8

Solving the Equation: (x+6)^(3/5) = 8

This equation involves a fractional exponent, making it a bit more complex than a simple linear equation. Let's break down the steps to solve for 'x'.

Understanding Fractional Exponents

Remember that a fractional exponent represents a combination of a root and a power. In this case, (3/5) means we're taking the fifth root and then cubing the result.

Solving the Equation

  1. Isolate the term with the fractional exponent: Since the entire term (x+6) is raised to the power (3/5), we need to isolate it first. This equation is already in this form.

  2. Eliminate the fractional exponent: To get rid of the (3/5) exponent, we need to raise both sides of the equation to the reciprocal power, which is (5/3).

    [(x+6)^(3/5)]^(5/3) = 8^(5/3)

  3. Simplify: The exponents cancel out on the left side, leaving us with:

    x + 6 = 8^(5/3)

  4. Calculate the right side: Calculate 8^(5/3). This means finding the cube root of 8 (which is 2) and then raising it to the power of 5.

    x + 6 = 2^5
x + 6 = 32

  5. Solve for x: Subtract 6 from both sides to isolate 'x'.

    x = 32 - 6 
x = 26

Solution

Therefore, the solution to the equation (x+6)^(3/5) = 8 is x = 26.

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