Hello there. To solve this question, we'll need some properties from powers:
First, something to the 0-th power is equal to 1:
[tex]a^0=1[/tex]
Second, multiplying powers of the same base is equal to keeping the base and adding the powers:
[tex]a^b\cdot a^c\cdot a^d\ldots=a^{b+c+d+\cdots}[/tex]
Third, dividing powers of the same base is equal to keeping the base and subtracting the powers:
[tex]\frac{a^b}{a^c}=a^{b-c}[/tex]
For the first question.
(-3^(-2))^0, applying the first rule, it will be equal to 1.
For the second question, keeping the base and adding the powers, we have:
[tex]3^3\cdot3^1\cdot3^2\cdot3^{-12}=3^{3+1+2-12}=3^{-6}=\frac{1}{729}[/tex]
For the third question, keeping the base and subtracting the powers, we have:
[tex]\frac{-3^5}{-3^8}^{}=^{}3^{5-8}=3^{-3}=\frac{1}{27}[/tex]
Finally, for the fourth question, keeping the base and adding the powers, we have:
[tex]-3^{-3}\cdot3^{-3}=-3^{-3-3}=-3^{-6}=-\frac{1}{729}[/tex]
