Question

2(x-2)^1/4-3-159

solve the radical or rational exponent equation

Answer 1

To solve the equation, distribute the exponent to both terms inside the parentheses, combine like terms, isolate the term with the exponent, raise both sides of the equation to the 4th power, simplify the equation, distribute 16, add 32 to both sides, and divide both sides by 16.

Step-by-step explanation:

To solve the equation, we can follow these steps:

1. Distribute the exponent to both terms inside the parentheses: 2(x-2)^(1/4) - 3 - 159
2. Combine like terms: 2(x-2)^(1/4) - 162
3. Isolate the term with the exponent by subtracting 2 from both sides: 2(x-2)^(1/4) = 162
4. Raise both sides of the equation to the 4th power to eliminate the fractional exponent: [2(x-2)^(1/4)]^4 = 162^4
5. Simplify the equation: 16(x-2) = 1465488
6. Distribute 16: 16x - 32 = 1465488
7. Add 32 to both sides: 16x = 1465520
8. Divide both sides by 16: x = 91670