solve each equation.\n36. $(5n - 6)^{\\frac{1}{3}}+3 = 4$\n38. $(6q + 1)^{\\frac{1}{4}}+2 = 5$\n40. $(3y…

Explanation:

Step1: Isolate the term with the exponent

For equation ((5n - 6)^{\frac{1}{3}}+3 = 4), subtract (3) from both sides: ((5n - 6)^{\frac{1}{3}}=4 - 3) ((5n - 6)^{\frac{1}{3}}=1)

For equation ((6q + 1)^{\frac{1}{4}}+2 = 5), subtract (2) from both sides: ((6q + 1)^{\frac{1}{4}}=5 - 2) ((6q + 1)^{\frac{1}{4}}=3)

For equation ((3y - 2)^{\frac{1}{5}}+5 = 6), subtract (5) from both sides: ((3y - 2)^{\frac{1}{5}}=6 - 5) ((3y - 2)^{\frac{1}{5}}=1)

Step2: Eliminate the exponent

For ((5n - 6)^{\frac{1}{3}}=1), cube both sides. Using the property ((a^{m})^{n}=a^{mn}), (\left((5n - 6)^{\frac{1}{3}}\right)^{3}=1^{3}) (5n-6 = 1) Add (6) to both sides: (5n=1 + 6), (5n=7), then (n=\frac{7}{5})

For ((6q + 1)^{\frac{1}{4}}=3), raise both sides to the (4^{th}) power. (\left((6q + 1)^{\frac{1}{4}}\right)^{4}=3^{4}) (6q+1 = 81) Subtract (1) from both sides: (6q=81 - 1), (6q=80), then (q=\frac{80}{6}=\frac{40}{3})

For ((3y - 2)^{\frac{1}{5}}=1), raise both sides to the (5^{th}) power. (\left((3y - 2)^{\frac{1}{5}}\right)^{5}=1^{5}) (3y-2 = 1) Add (2) to both sides: (3y=1 + 2), (3y=3), then (y = 1)

Answer:

For (n): (n=\frac{7}{5}) For (q): (q=\frac{40}{3}) For (y): (y = 1)