If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Integrated math 2>Unit 6

Lesson 3: Equivalent forms of exponential expressions

# Equivalent forms of exponential expressions

Sal rewrites (1/32)*2^t as 32*1024^(t/10-1).

## Want to join the conversation?

• Look, I've come a long way in my maths learning thanks to Sal, but this particular module on exponents is honestly pretty bad. The practice questions involve techniques not covered in the videos, and the videos gloss over important details.

The only reason I've been able to follow up until this point is because I recently did a small course on exponents, and learned the properties of exponents formulas. Here, the formulas aren't explicitly explained. They're just mentioned as side notes. I found I developed far better intuition when starting with the properties, then going into examples of why they work the way they do.

Perhaps it's just my learning style, but I found this module to be badly thought out.
• You should put this post in the Tips and Thanks section and give your thoughts or any suggestions!
just do this in a respectful tone!
(1 vote)
• at what does "hairy" mean? does it mean complicated?
• I believe it does mean complicated in this context.
• Can I get some help with ((2/3)^x+4) -(2/3)^x? This is one of the exercise problems, and I don't quite understand the hint. I understand everything up to the point where 2/3^x * 15/16 -2/3^x. The next hint shows (2/3^x) * (15/16-1). I don't know where the -1 came from nor what happened to the other 2/3^x. I understand that you can factor a -1 out of -2/3^x.
• Here is why 2/3^x * 15/16 -2/3^x becomes (2/3^x) * (15/16-1):

Let's use a different example. Look at the expression (9*3)-9 (which equals 18). Notice, we multiply 9 by 3 to get a total of three "nines" (which equal 27), then subtract a nine to get only two "nines" (which equal 18). Nine times two equals eighteen. Thus, (9*3)-9 is the same thing as 9*(3-1), or 9*2.

In the example above, we have 15/16 "2/3^x"s and are subtracting one "2/3^x". Thus, the expression is equal to (2/3^x) * (15/16-1). I hope I explained it well!
• i've been doing these practice problems for over a combined 8 hours and still cant get more than 2 out of 4 questions right.. I can usually almost complete a full unit in this timeframe.. I never know when to use what.. how can i get better?
• I reccomend looking at the way they solve the problem, though it isn't always helpful, it might be helpful in your case, after 4 tries I managed to get a 3/4!
• At , I'm confused at why 1034 is over 32. How did that happen?
• First, it's 1/32*(1024^(t/10-1))*1024, and sal said that he want it in the A*B^x form. So he want to multiply 1/32 and 1024 together to form A then multiply (1024^(t/10-1)) to get that A*B^x form.

And 1/32*1024 = 1024/32

Hop that helps!
• hello, i am very confused on this practice section. I don't understand how you find which expressions are similar. ive watched the video like 20 times but it doesnt cover what is asked in the practice.
• Wait... isn't a^1 the same as if it was a^(-1)? Just a random thought while watching this video. Logically it makes sense. The root of one is the number itself as the regular exponent, thus it sould be the same.
• a^1 = a
a^(-1) = 1/a (the reciprocal of a)
Hope this helps.
• How would you write -3^2 in expanded form?
How would you write (-3)^2 in expanded form?
(1 vote)
• Because of the order of operations BEDMAS (or whichever letters you have been taught), you need to do the brackets first and then the exponents.

For -3^2, there are no brackets so the exponent has priority. That means you do 3^2 first and then add the minus. This gives an answer of -9. If you were to add brackets, this would have been written as -(3^2).

For (-3)^2, you need to realise that there are brackets. This shows that the entire -3 (including the minus sign) is being squared. When you square a number, you multiply it by itself. (-3)x(-3) is equal to 9 because multiplying a negative number with another negative number always gives a positive number.

Therefore, in expanded form:
-3^2 = -(3x3) = -9
(-3)^2 = (-3)x(-3) = 9

This is a great example to illustrate the importance of adding brackets to avoid getting different answers! :)

Hope that helps!
• I have a question, when you move exponents from one side of the equation to the other do you inverse it? I found that I could have inversed an exponent from the previous exercise to get the answer, and it also seems to show in this video. I also remember my math teacher mentioning this before. How does that work? Is there a faster way to do this?
(1 vote)
• Yes. For example
10^5 = x
10 = x^(1/5)
This is kind of like square rooting, but instead of square, you take a higher root. I believe inversing it is the fastest way to do so.