SOLUTION: what does this mean (1*.01)^36 = 1E-72

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Question 955755: what does this mean (1*.01)^36 = 1E-72
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
what does this mean (1*.01)^36 = 1E-72
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(1*.01)^36 = 0.01^36
= %2810%5E%28-2%29%29%5E36
= 10%5E%28-72%29
= 1e-72 (a more convenient way of writing it)

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the laws of exponents state:

x%5Ea+%2A+x%5Eb+=+x%5E%28a%2Bb%29

%28x%5Ea%29%5Eb+=+x%5E%28a%2Ab%29

%28x%5Ea%2Ay%5Eb%29%5Ec+=+x%5E%28ac%29+%2A+y%5E%28bc%29

x%5E%28-a%29+=+1%2Fx%5Ea

x%5Ea+=+1%2Fx%5E%28-a%29

your equation states:

%281%2A.01%29%5E36+=+1E-72

since (1 * .01) is the same as (.01), your equation becomes:

%28.01%29%5E36+=+1E-72

1E-72 is the same as 1 * 10^(-72)

that's what it means.

your equation becomes:

%28.01%29%5E36+=+1+%2A+10%5E%28-72%29

.01 is the same as 1/100 which is the same as 1/10^2 which is the same as 1 * 10^(-2).

your equation becomes:

%281+%2A+10%5E%28-2%29%29%5E36+=+1+%2A+10%5E%28-72%29

since %281+%2A+10%5E%28-2%29%29%5E36 is equivalent to 1%5E36+%2A+%2810%5E%28-2%29%29%5E36, your equation becomes:

1%5E36+%2A+%2810%5E%28-2%29%29%5E36+=+1+%2A+10%5E%28-72%29

since 1^36 is equal to 1, your equation becomes:

1+%2A+%2810%5E%28-2%29%29%5E36+=+1+%2A+10%5E%28-72%29

since %2810%5E%28-2%29%29%5E36 is equal to 10%5E%28-2%2A36%29, your equation becomes:

1+%2A+10%5E%28-2%2A36%29+=+1+%2A+10%5E%28-72%29

since 10%5E%28-2%2A36%29 is equal to 10%5E%28-72%29, your equation becomes:

1+%2A+10%5E%28-72%29+=+1+%2A+10%5E%28-72%29

the equation is true because the left side is equal to the right side.

you have proven that:

(1*.01)^36 = 1E-72