How do I solve this equivalent expression?

3^-5 is not equal to 1/3^-5.  Remember that the sign of the exponent changes when you create a fraction.

3^-5 is equal to 1/3^5.

Can you get to the next step from there?

Well, what AD Baker says is correct, but also, you can see it like this:

3^-5
= 1/3^5 (I just created a fraction to change the sign of the exponent)
= 1^5/3^5 (then, I think you agree that 1^5 = 1, so I just made that change)
= (1/3)^5 (Finally, the last change that I made, it was just for use the property that says (a^x/b^x)=(a/b)^x)
And we're done!

Stay happy, sweet and healthy!

@ADBaker, @Yahir.Q: Thanks for trying to help me figure this out!

I'm stuck at step 3. How did you get 1^5? 

Here's my not-so-good attempt at trying to rewrite the problem to understand.

Ok. In the first picture, you get to the 1^5 just because you know that 1 at the power of any positive integer number, that always is going to be 1, and yes, you could use:

• 1^2 = 1
• 1^3 = 1
• 1^4 = 1
• 1^5 = 1
• 1^6 = 1
• and so on.

I mean:

From the step two: 1/3^5 = 1^(any positive integer number)/3^5
Because the numerator and denominador are the same. 
Numerator: 1 = 1^(any postive integer number)
Denominador: 3^5 = 3^5

Now, whit that clear (let me know if it wasn´t clear please with a "hold on" phrase or whatever), to use the properite of a quotient, that says:

(a^x/b^x)=(a/b)^x and viceversa.

that you can find here:

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-exponent-properties/a/exponent-properties-review

then, just because you want to use that property, you'll choose the 1^5, thus:

(a^x/b^x)=(a/b)^x 
1^5/3^5 = (1/3)^5

And that´s why and how you get that. Hope this helps and please ask me if something you still can´t understand.

Yahir.Q Thanks for directing me to that link.

I went back and revisted the lesson "Exponent Properties with Products".

Your explanation, plus this video has helped me to understand.