Question

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Answer 1

Hello there. To solve this question, we'll need some properties from powers:

First, something to the 0-th power is equal to 1:

`a^0=1`

Second, multiplying powers of the same base is equal to keeping the base and adding the powers:

`a^b\cdot a^c\cdot a^d\ldots=a^(b+c+d+\cdots)`

Third, dividing powers of the same base is equal to keeping the base and subtracting the powers:

`(a^b)/(a^c)=a^(b-c)`

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:

`3^3\cdot3^1\cdot3^2\cdot3^(-12)=3^(3+1+2-12)=3^(-6)=(1)/(729)`

For the third question, keeping the base and subtracting the powers, we have:

`(-3^5)/(-3^8)^{}=^{}3^(5-8)=3^(-3)=(1)/(27)`

Finally, for the fourth question, keeping the base and adding the powers, we have:

`-3^(-3)\cdot3^(-3)=-3^(-3-3)=-3^(-6)=-(1)/(729)`