I need steps on how to solve a fraction as an exponent. 2/3(9)3/2

Thank you! This might be a stupid question... but how do you algebraically solve the part where you divide A sub n+1 by a sub n?  How did you get 1+(3^n)+3 in the numerator? I thought the answer would be 2n(1+3^n+1)? Please explain that. I didn't understand that during class either.

I am using MyMath lab for basic algebra. I do not understand how to work this problem and the example does not give an easily understood explanation. I'm not sure how to type a fraction on here, but the numbers in the parenthases is a fraction.    (-2/13)x = -10.2   I know to multiply each side by the reciprocal, which is (-13/2) I do not understand how to accurately multiply the reciprocal of the fraction and the decimal.  I am sure I am overthinking this, but any help would be greatly appreciated.

Explain why 4 = 4 using the relationship between radical expressions, rational exponents, and properties of exponents Type your answer in the box Use the √z button to enter math expressions and equations.