Answer and Step-by-step explanation:
Alot of these can be solved with the table up above the problems.
A, B, and C.
According to the table, every time a value has an exponent of 0, it would equal to 1. Since all A B and C values follow the 0 exponent, their value is 1.
D.
According to the table, when we have a negative exponent, the number gets turned into a fraction of
![(1)/(x^x)](https://img.qammunity.org/2022/formulas/mathematics/high-school/eykljsxffo3ngxo76c8cns29badok35fu6.png)
Since our value is 9^-2, do as followed :
![(1)/(9^2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/m3stagwd8z40drcvdlq7debildyp13ax74.png)
Solve what is 9^2 :
![[(1)/(81) ]](https://img.qammunity.org/2022/formulas/mathematics/high-school/v199d0veu5e6tzazsr835qyc7ask5fjw2l.png)
E.
![(1)/(x^(-5) )](https://img.qammunity.org/2022/formulas/mathematics/high-school/5rn1h5kcpqbunlrtnwqiyancyozdctibas.png)
This question is different, since we have to go backwards, we have to switch the negative exponent to a positive exponent and rid the fraction.
![x^5](https://img.qammunity.org/2022/formulas/mathematics/high-school/gh2upnt5y9geqzoa2gqeebdew5b4m8uucn.png)
F.
![5a^3b^(-2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/eucml05ntis00dpe6gzgh17qi3tq39lmyt.png)
Since we have one negative exponent, follow the fraction rule but instead of having one as the numerator, have 5a^3.
![(5a^3)/(b^(2))](https://img.qammunity.org/2022/formulas/mathematics/high-school/3rdbl62y62b400tolz45hv32kr3zfoy26h.png)
Fill in the table :
![-3^4 = -3*-3*-3*-3=-81](https://img.qammunity.org/2022/formulas/mathematics/high-school/1peiot46n6251wyzhittfdhiwyu89bb2s6.png)
Since -3 is in parenthesis, we can rid the negative along with the parenthesis :
![(-3)^4=3^4=3*3*3=81](https://img.qammunity.org/2022/formulas/mathematics/high-school/y3i81r6z89ocefgahi5d7nnrorexwmdm2t.png)
Follow the negative exponent rule :
![(-3)^(-4)=(1)/((-3)^4) =(1)/(3^4) =(1)/(3*3*3*3)= (1)/(81)](https://img.qammunity.org/2022/formulas/mathematics/high-school/g9bgkurxkvs75t4jzhd7bpk1qpw0zdmho2.png)
Follow the negative exponent rule yet again :
![-3^(-4)=-(1)/(3^4) =-(1)/(3*3*3*3) =-(1)/(81)](https://img.qammunity.org/2022/formulas/mathematics/high-school/j7mojpzrnz7oo622xitx2r8ysw7v6biqac.png)