Question

Zero and Negative Exponents / All of the LeftEvaluate each of the following expressions:

Answer 1

1.

`\begin{gathered} 5^0 \\ In\text{ indices, any entity raise to the power of zero is always 1.} \\ a^0=1 \\ \text{Therefore:} \\ 5^0=1 \end{gathered}`

3.

`\begin{gathered} 24^0 \\ \text{This follows the explanation of the above question:} \\ a^0=1 \\ 24^0=1 \end{gathered}`

5.

`\begin{gathered} 9^(-2) \\ To\text{ solve this, we will follow the indices law that:} \\ a^(-b)=(1)/(a^b) \\ \text{Therefore:} \\ 9^(-2)=(1)/(9^2) \\ =(1)/(81) \end{gathered}`

9.

`\begin{gathered} 6^(-4)\cdot6^4 \\ In\text{ indices, the law that applies to the above expression:} \\ a^b\cdot a^c=a^(b+c) \\ \text{Therefore:} \\ 6^(-4)\cdot6^4 \\ =6^(-4+4) \\ =6^0 \\ =1 \end{gathered}`

7.

`\begin{gathered} (1)/(2^(-3)) \\ In\text{ indices, this takes the form:} \\ (1)/(a^(-b))=a^b \\ \text{Therefore}\colon \\ (1)/(2^(-3)) \\ =2^3 \\ =8 \end{gathered}`

11.

`\begin{gathered} (-3\cdot2)^(-2) \\ =(-3*2)^(-2) \\ =(-6)^(-2) \\ In\text{ indices, } \\ a^(-b)=(1)/(a^b) \\ \text{Therefore:} \\ =(-6)^(-2) \\ =(1)/(-6^2) \\ =(1)/(36) \end{gathered}`