solve the equation with rational exponents. check all proposed solutions.\n4x^(9/5) - 20 = 0\nselect the…

solve the equation with rational exponents. check all proposed solutions.\n4x^(9/5) - 20 = 0\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the solution set is \n(type an exact answer in simplified form. use a comma to separate answers as needed.)\nb. the solution set is ∅.

solve the equation with rational exponents. check all proposed solutions.\n4x^(9/5) - 20 = 0\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the solution set is \n(type an exact answer in simplified form. use a comma to separate answers as needed.)\nb. the solution set is ∅.

Answer

Explanation:

Step1: Isolate the term with x

Add 20 to both sides of the equation $4x^{\frac{9}{5}}-20 = 0$. $4x^{\frac{9}{5}}=20$

Step2: Solve for $x^{\frac{9}{5}}$

Divide both sides by 4. $x^{\frac{9}{5}}=\frac{20}{4}=5$

Step3: Solve for x

Raise both sides to the $\frac{5}{9}$ power. $x = 5^{\frac{5}{9}}$

Answer:

A. The solution set is $5^{\frac{5}{9}}$