Solve for x (x-15)^(3/4)=27

Problem

(x−15)(3/4)=27

Solution

1. Isolate the base by raising both sides of the equation to the reciprocal power of 3/4 which is 4/3

((x−15)(3/4))(4/3)=27(4/3)

2. Simplify the left side using the power of a power rule, (am)n=a(m*n) which leaves the expression inside the parentheses.

x−15=27(4/3)

3. Evaluate the numerical expression on the right side by taking the cube root of 27 and then raising the result to the fourth power.

x−15=(√(3,27))4

4. Calculate the value of the root and the exponent.

x−15=3

x−15=81

5. Solve for x by adding 15 to both sides of the equation.

x=81+15

x=96

Final Answer

(x−15)(3/4)=27⇒x=96

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