Solve for x x^(5/2)=32

Problem

x(5/2)=32

Solution

1. Identify the equation as a power equation where the variable x is raised to the exponent 5/2

2. Isolate the variable x by raising both sides of the equation to the reciprocal of the exponent, which is 2/5

(x(5/2))(2/5)=32(2/5)

3. Apply the power of a power rule on the left side, which simplifies the exponent to 1

x=32(2/5)

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

x=(√(5,32))2

5. Evaluate the fifth root of 32 noting that 2=32

x=2

6. Simplify the final numerical value.

x=4

Final Answer

x=4

Want more problems? Check here!