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Describe any patterns/relationships that you notice between the Powers of 10, the expressions, what they equal (standard form), or amount of zeros in the product. Try to use math vocabulary in your explanation below. You may use examples to support your response.

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Answer:

The powers of 10 are things of the form:

10^n.

Where we assume that n is an integer number.

if is equal or larger than 0, then:

We add n zeros at the right of the 1.

so let's write some examples.

10^0 = 1 (we do not add any zero)

10^1 = 10 (we add one zero)

10^2 = 100 (we add two zeros)

...

Now, remember that x^-y = 1/x^y, then:

If n is smaller than zero, then we add n zeros at the left of the 1.

10^-1 = 1/10 = 0.1 (one zero at the left)

10^-2 = 1/100 = 0.01 (two zeros at the left).

Those relations will be useful to always know the exact dimensions of the powers of zero.

Now, we can give a more complete description knowing that:

x^a*x^b = x^(a + b)

Then if we have:

10^3*10^4 = 100*1,000 (and this may be hard to do)

But we can use the above relation:

10^3*10^4 = 10^(3 + 4) = 10^7

Then we know that we must add 7 zeros at the right of the 1.

And this will work for any integer powers of 10.

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