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# Differential Equations/Help

Question
Hello sir

what is the difference between exponents and multiplication.

Multiplication is multiplication, as in 2*4 = 8, 13*4 + 52, 7*9 = 63, etc.

When the same numbers are used as exponents, as in A^B, it means to multiply A by itself B times.  To see the last response with the numbers as exponents, they are written as
2^4 = 2*2*2*2 = 16, 13^4 = 13*13 * 13*13 = 169 * 169 = 28,561;
7^9 = 7*7*7 * 7*7*7 * 7*7*7 = 343 * 343 * 343 = 117,649 * 343 = 40,353,607.

Exponents are how many times to multiply a number by itself.
Note that 3^2 = 3*3 = 9; 3^4 = 3*3 * 3*3 = 9*9 = 81;
5^6 = 5*5 * 5*5 * 5*5 = 25*25 * 25 = 625*25 = 15,625.

Now as far as exponents go, there are a couple of curious cases to see.
The first is 1^1 = 1*1 and 2^2 = 2*2. When 1 or 2 is used, the power sign and the multiplication sign are interchangeable, but these are the only two cases where that occurs.

Also note that there is another special case.  That is 2^4 = 4^2 = 16.  Here the 2 and 4 can be reversed, but as I said, that is the only case I know of where the numbers can be swapped.

Differential Equations

Volunteer

#### Scott A Wilson

##### Expertise

I am capable of solving most ordinary differential equations and a few not so ordinary, but those are few and far between.

##### Experience

I have taken Differential Equations at OSU. Occasionally I have assisted people with questions on the subject.

Publications
I wrote a thesis on the study of shock waves and rarefaction fans. That occurs in nature when mathematics fails to apply. See, mathematics says that when shock waves appear, there should be two solutions whereas nature knows there is only one way to be in that area. When rarefaction fans occur, the mathematics says there should be no solution, but despite this, nature still moves ahead with its own plan.

Education/Credentials
I received an MS degree at OSU in Mathemematics and a BS degree at OSU in Mathematical Science.

Awards and Honors
I graduated from OSU with a Bachelor of Science degree in mathematics with honors. Two years later, I graduated from OSU with a Master of Science degree in mathematics with honors. Between these two degrees, I have more hours in graduate courses that required to get them.

Past/Present Clients
I answered many questions at OSU, down in south seattle at a college, at a church in Corvallis, OR, as Safeway in Washington, and many other areas. I have answered over 8,500 right here, but only a little over 190 of them have been in differential equations.