Can you pass this Harvard Entrance Exam?|98%failed|Exponential simplification

A Harvard Entrance Exam. This is one of the hardest and trickiest questions that I have solved so far. It is easy but tricky. #maths #harvard #math #entranceexam #exponents.
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[@key_board_x]

= √[9^(9⁹)] → we know that: √a = a^(1/2)
= [9^(9⁹)]^(1/2) → we know that: [x^(a)]^(b) = x^(ab)
= 9^[9⁹ * (1/2)] → we know that: 9⁹ = 9 * 9⁸
= 9^[9 * 9⁸ * (1/2)] → we can order the multiplication: a * b * c = b * c * a
= 9^[9⁸ * (1/2) * 9]
= 9^[9⁸ * (9/2)]
= 9^[9⁸ * 4.5] → we can twist the items once again
= 9^[4.5 * 9⁸]
d) answer

[@RyanLewis-Johnson-wq6xs]

Surd[8,3]=2

[@RyanLewis-Johnson-wq6xs]

4^(1/2)=2

[@RyanLewis-Johnson-wq6xs]

Sqrt[4]=2

[@MackensonMerilus-e4z]

Great!

[@RyanLewis-Johnson-wq6xs]

I said d) 9^(4.5*9^8) final answer.

[@JJONLINEMATHSCLASSchannel]

👍👍

[@nickronca1562]

The answer can also be 3^9^9

[@denzilgounden4044]

9=3^2 therefore 3^2/2^9^9 therefore the answer is 3^9^9

[@JJONLINEMATHSCLASSchannel]

You tried but you are wrong

[@denzilgounden4044]

i think I'm right

[@denzilgounden4044]

@@JJONLINEMATHSCLASSchannel When I put your equation and my answer in the calculator I get exactly the same answer but If I put your answer in the calculator it says Invalid input , , pls try it

[@nickronca1562]

​@@JJONLINEMATHSCLASSchannelLmao, he is right

[@rishicadavid2968]

Hi what are some good text books for arithmetic and pre algebra

[@RyanLewis-Johnson-wq6xs]

8^(1/3)=2