Solve for y y^(4/5)=34

Problem

y(4/5)=34

Solution

1. Identify the equation as a power equation where the variable y is raised to the exponent 4/5

2. Isolate the variable y by raising both sides of the equation to the reciprocal of the exponent, which is 5/4

(y(4/5))(5/4)=34(5/4)

3. Apply the power of a power rule, (am)n=a(m⋅n) to the left side to simplify the exponent to 1

y=34(5/4)

4. Rewrite the expression using radical notation if necessary, noting that 34(5/4) can be expressed as the fourth root of 34 raised to the fifth power.

y=√(4,34)

5. Simplify the radical by extracting factors. Since 34=34⋅34 the fourth root of 34 is 34

y=34√(4,34)

Final Answer

y=34√(4,34)

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