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Rudik [331]
3 years ago
5

Why can’t we use the rules for exponents when the bases are not common?

Mathematics
1 answer:
Kazeer [188]3 years ago
4 0

Answer:

Ok, the rules of the exponent come from a logic construction.

If we have x^n

this means that n is multiplied by itself n times.

If we decompose n into a + b, we have:

x by itself a times, and then x by itself b times, and for how the product works, this is equivalent:

if n = 5, a= 2 and b = 3

x^5 = (x*x*x*x*x)   5 times-

x^5 = x^(2 + 3) = (x^2)*(x^3) = (x*x*)*(x*x*x) = x*x*x*x*x = x^5

And the same for the other rules:

(x^n)^b = x^n*b and such.

Obviusly, this only works when we have a common base.

So the correct answer is that we constructed the exponential rules in a way that only can be used when we have a common base, and this happens because to construct them, we started with common bases.

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The decimal place accuracy of a number is the number of digits to the right of the decimal point. The decimal point is a period written between the digits of a number. If there is no decimal point, it is understood to be after the last digit on the right and there is no place (zero place) accuracy.

The significant digits of a number are those digits that are most accurate. If a number has no place accuracy and there is no string of zeroes ending the number on the right, all the digits are significant. If a number has no place accuracy and there is a string of zeroes ending the number on the right, the significant digits are those digits to the left of the string of zeroes. If a number has a decimal point, the significant digits are the digits starting from the first non-zero number on the left to the last digit written at the right end. In either case the number of significant digits is just the count of these digits.

Decimal notation is the regular written format for a number. Scientific notation of a number just writes the significant digits followed by an appropriate power of ten.

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Step-by-step explanation:

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