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## Algebra (all content)

### Course: Algebra (all content)>Unit 11

Lesson 15: Equivalent forms of exponential expressions

# Rewriting exponential expressions as A⋅Bᵗ

Sal simplifies the expression 10*9^(0.5t+2)*5^(3t) as 810*375^t.

## Want to join the conversation?

• At Sal gets the answer for 9^1/2 as 3. How does that work? How do you raise a number to a fractional exponent?
• 9^(1/2) is equivalent to the square root of 9. For a fractional exponent, the denominator is the nth root, and the numerator is the power. For example 9^(3/2) is sqrt(9^3).
• Hello, I have been having a problem in the next practice. I don't know how to do problems that look similar to this one;
(5/2)^x + (5/2)^(x+3) = A * (5/2)^x
I know that this simplifies into,
(5/2)^x + (5/2)^x * (125/8),
but I have no idea how to get the expression,
(5/2)^x ((125/8) + 1).
(5/2)^x + (5/2)^x*(125/8)
Everything is multiplied by an invisible one.
(5/2)^x*1+(5/2)^x*(125/8)
If it is this number*_+ this number*__ we can add the _+__ and multiply it by this number. So when it is simplified the end expression is:
this number*(_+__).
If you apply it to this expression, the end result is:
(5/2)^x*((125/8) + 1).
I hope this explanation isn't to confusing.
If you need help understanding it, please comment.
• Anyone else find that the video doesn't prepare them to tackle the practice exercises? There seems to be a missing step.
• Yes that's true,but I don't think that is important
• The practice problems have nothing to do with the video...we were never taught how to do the practice problems.
• Is anyone able to recommend any videos from any source that explains the concepts in the practice exercises? Like rewriting exponential expressions in a certain way? I really need instructions on how to do this, not just how to solve 1 particular problem like these videos show. In this video, he just happened to get lucky in finding the correct form that the question was asking. How do you manipulate an expression to the proper form without taking random shots in the dark? Thanks for any help!
• This was the only video I could find that seemed somewhat helpful: https://www.youtube.com/watch?v=gyz0vyykiSw
• Sal said 9 ^ 1/2 = 3. Is there any way to express like 9 ^ (something) = -3 ?
• Only imaginary numbers can satisfy that equation.
• I got nothing from the video, can someone give me a brief-but yet understandable explanation of the concept Sal is trying to explain? Thank you and have a great day! :D
• Howdy Joseph,

When writing an exponential expression it is usually the most convenient to have it in the form of A * B^t, where A and B are any real numbers.

In this video, Sal was giving examples of using some exponent properties to help show how to rewrite exponential expressions.

Exponential Propertes
Here are some exponential properties that you should be familiar with.
a^(bc) = (a^b)^c // or vice versa
a^b * a^c = a^(b + c)
a^b / a^c = a^(b - c)
a^c * b^c = (a*b)^c

Once you know those exponential properties, we can use them to simplify our exponential expressions to a more simpler form, preferably A*B^t.

Now that you know what Sal is trying to do, it may be advisable to rewatch the video and get some practice rewriting exponential expressions.

Happy learning! :-)