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Answer 1

So for the first one, when it comes to multiplying exponents, you are allowed the exponents. When they are being raised to another exponent, they are multiplied, so:

\[\large 3^2*(3^3)^2*3^{-8}=3^2*3^6*8^{-8}\]
Simplify it as such:
\[\Large 3^{2+6+(-8)}= 3^0\]

Answer 2

When it comes to dealing with division of exponents, you're gonna need to subtract exponential powers if one is in the denominator while the other is in the numerator:
\[\large \frac{3^2*(2*3)^{-3}}{2^{-3}}\]
With this, you're gonna need to flip the negative exponent on the top and bring to the denominator:
\[\Large \frac{3^2}{2^{-3}*(2*3)^{3}}\]
Distribute the exponent:
\[\Large \frac{3^2}{2^{-3}*2^3*3^3}\]
Simplify:
\[\Large \frac{3^2}{1*3^3}= 3^{2-3}=3^{-1}=\frac{1}{3}\]

Answer 3

Ignore that 8^-8, it's suppose to be a 3^-8