Solve for x x^(3/4)=125

Problem

x^(3/4)=125

Solution

1. Identify the equation as a power equation where the variable x is raised to a rational exponent.

2. Isolate the variable x by raising both sides of the equation to the reciprocal of the exponent, which is 4/3

(x^(3/4))^(4/3)=125^(4/3)

3. Simplify the left side using the power of a power rule, (a^m)^n=a^(m⋅n) which leaves x^1

x=125^(4/3)

4. Rewrite the right side using the definition of rational exponents, a^(m/n)=(√(n,a))^m

x=(√(3,125))^4

5. Evaluate the cube root of 125

√(3,125)=5

6. Calculate the final value by raising the result to the power of 4

x=5^4

x=625

Final Answer

x^(3/4)=125⇒x=625

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