   SEARCH HOME Math Central Quandaries & Queries  Question from Emily, a student: For my Math homework, my pre-algebra2, I have to write the Exponential Form of 125 x 25 and 81x 27. How should I write those in the exponential form??? -Emily Hi Emily.

Exponential form is, as you probably guessed, a form that shows exponents.

Let me give you a sample so you can try those two questions yourself.

Write in exponential form: 128 x 32.

First I have to decide if each of these numbers is a power of another number. I know 4 x 4 is 16 and 16 x 2  is 32. So 32 = 2 x 2 x 2 x 2 x 2  = 25. Also I know that 128 is 32 x 4, so 128 is 25 x 2 x 2 = 27. Thus,

128 x 32 = 25 x 27.

The last step is to realize that if two factors have the same base (in this case, both bases are 2), then you can add the exponents:

25 x 27 = 25+7= 212.

And that is in exponential form. So the final answer is

128 x 32 = 212.

Now you try the same idea with your questions.

Cheers,
Stephen La Rocque     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.