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, (a^m)^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)

5. Simplify the radical by extracting factors. Since 34^5=34^4⋅34 the fourth root of 34^4 is 34

y=34√(4,34)

Final Answer

y=34√(4,34)

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