a) Exponential expressions have the next form:
![b^x](https://img.qammunity.org/2023/formulas/mathematics/high-school/4tzokq0330c3oc46ljrl3sahuqpsgkjyqz.png)
where b is the base and x is the exponent. Substituting with b = -8 and x = 3, we get:
![(-8)^3=-512](https://img.qammunity.org/2023/formulas/mathematics/high-school/gsnetao4kuijueixzg296zcxjdrwrllt9m.png)
b) In this case, the base is -2 and the exponent is 4:
![(-2)^4=16](https://img.qammunity.org/2023/formulas/mathematics/high-school/q4cpwvwz101hbbjkzjnfg553swpvm34vsp.png)
c) In this case, the base is 30 and the exponent is 2:
![30^2=900](https://img.qammunity.org/2023/formulas/mathematics/high-school/u6970z9hrpzdfnryu2fld57ob9cxqr4jyn.png)
d) In this case, the base is 0 and the exponent is 100:
![0^(100)=0](https://img.qammunity.org/2023/formulas/mathematics/high-school/8kzaxy051fgvj9g6mpjqb7mspaov85xgfp.png)
Note that when the base is zero, the value of the expression is also zero.
e) In this case, the base is 9 and the exponent is 3:
![9^3=729](https://img.qammunity.org/2023/formulas/mathematics/high-school/remaxgdcftpaseay03f5te8icbxfo1gcrn.png)