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User Luis LL
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Exponential function

Part A

We know that


2^6=64

then


\begin{gathered} (2^6)^x=1 \\ 64^x=1 \end{gathered}

then, we want to find a value of x so if we multiply x times 64 it will be 1.

We know that any number with exponent 0 is 1:


64^0=1

Then x = 0

Part B

Since any number with exponent 0 is 1, then:


5^0=1

Then,


\begin{gathered} (5^0)^x=1 \\ 1^x=1 \end{gathered}

So, we want to find a number for x so if 1 is multiplied x times it will be 1.

Everytime 1 is multiplied by itself the answer is 1:


\begin{gathered} 1^2=1\cdot1=1 \\ 1^4=1\cdot1\cdot1\cdot1=1 \\ 1^(-2)=(1)/(1)\cdot(1)/(1)=1 \end{gathered}

Then, x is any number

x = ..., -2, -1, 0 , 1, 2, ...

User UrbanoJVR
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