a) We want to calculate:
[tex]9^6[/tex]
We can write the last equation in the following form:
[tex]9^{1+5}=9^1\cdot9^5=9\cdot(9^5)=9\cdot(9^2\cdot9^3)[/tex]
Where we have used the laws of exponents. Now we can replace the terms inside the parenthesis with the equation of the statement and find that:
[tex]9\cdot(9^2\cdot9^3)=9\cdot59049=531441[/tex]
Where in the last step we just multiplied 9 with 59049.
b) We consider:
[tex](81)^3=531441[/tex]
We know that: 81 = 9*9 = 9^2 , so using that, and the laws of exponents we conclude that:
[tex](81)^3=(9\cdot9)^3=(9^2)^3=9^{2\cdot3}=9^6^{}^{}[/tex]
So:
[tex]9^6=531441[/tex]
