Answer:
x = 126
Step-by-step explanation:
Using the rule of exponents/ radicals
[tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^{m} }[/tex]
Given
[tex](x-1)^{\frac{2}{3} }[/tex] - 25 = 0 ( add 25 to both sides )
[tex](x-1)^{\frac{2}{3} }[/tex] = 25 ( raise each side to the power of 3 )
(x - 1)² = 25³ = 15625 ( take the square root of both sides )
x - 1 = [tex]\sqrt{15625}[/tex] = 125 ( add 1 to both sides )
x = 126
