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Any number, positive or negative, raised to an even-numbered

power, returns a positive number.

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Q: What pattern do you discover when solving even-numbered exponents with negative bases?
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Why is any number raised to a negative power is what it is?

That is the way it is defined; in theory, it could be defined any other way. But the definition commonly used makes several rules maintain their validity, for example, the law about adding exponents - even when the exponent is negative.Consider this sequence:103 = 1000102 = 100101 = 10100 = 110-1 = 1/1010-2 = 1/100Every time the exponent is reduced by one, the result gets reduced by a factor of 10. So, it seems logical to continue this pattern for a zero or negative exponent. Mind you, this is no proof - after all, the negative exponents is a matter of definitions, not of proof. The above only merely shows that the definition is reasonable.That is the way it is defined; in theory, it could be defined any other way. But the definition commonly used makes several rules maintain their validity, for example, the law about adding exponents - even when the exponent is negative.Consider this sequence:103 = 1000102 = 100101 = 10100 = 110-1 = 1/1010-2 = 1/100Every time the exponent is reduced by one, the result gets reduced by a factor of 10. So, it seems logical to continue this pattern for a zero or negative exponent. Mind you, this is no proof - after all, the negative exponents is a matter of definitions, not of proof. The above only merely shows that the definition is reasonable.That is the way it is defined; in theory, it could be defined any other way. But the definition commonly used makes several rules maintain their validity, for example, the law about adding exponents - even when the exponent is negative.Consider this sequence:103 = 1000102 = 100101 = 10100 = 110-1 = 1/1010-2 = 1/100Every time the exponent is reduced by one, the result gets reduced by a factor of 10. So, it seems logical to continue this pattern for a zero or negative exponent. Mind you, this is no proof - after all, the negative exponents is a matter of definitions, not of proof. The above only merely shows that the definition is reasonable.That is the way it is defined; in theory, it could be defined any other way. But the definition commonly used makes several rules maintain their validity, for example, the law about adding exponents - even when the exponent is negative.Consider this sequence:103 = 1000102 = 100101 = 10100 = 110-1 = 1/1010-2 = 1/100Every time the exponent is reduced by one, the result gets reduced by a factor of 10. So, it seems logical to continue this pattern for a zero or negative exponent. Mind you, this is no proof - after all, the negative exponents is a matter of definitions, not of proof. The above only merely shows that the definition is reasonable.


What is an arithmetic pattern?

a arithmetic pattern is a mathmatical pattern, or sequence that helps us discover the patterns in increasing and decreasing numbers.


Is Fibonicci a pattern sequence?

Not sure about Fibonicci but the Pisan mathematician, Fibonacci, did discover a pattern sequence which was named after him.


What are the next two numbers in the pattern and what is the pattern 12500 negative 2500 500 negative 100?

Never mind guys I figured it out!


How did Mendeleev discover the pattern that led to periodic table?

something to do with protons and stuff.


What pattern Mendeleev discover when he arranges the elements?

A Pattern of properties appeared when he arranged the elements in order of increasing Atomic Mass


What pattern did Mendeleev discover when he arranged element?

A Pattern of properties appeared when he arranged the elements in order of increasing Atomic Mass


Which quote is correct - negative ghost rider or negative ghost writer?

It's from the TV show. The full quote is, "Negative, Ghost Writer - the pattern is full."


How can you recognize an exponential decay pattern from a graph?

When the graphdecreasesat a rapid rate. Instead of just a negative straight line it will be a negative half parabola decreasingextremelyfast and then leveling out.


Positive or negative decimals that are nonterminating and nonrepeating or have a pattern in their digits but do not repeat exactly are?

Irrational numbers.


Why does a negative number times a negative number have a positive product?

If I were you, I'd ask the same thing. When you're multiplying with different signs, the product will always change. Think of it as this... There is 1 negative. So it's a negative. But when there's 2 negatives, it's a positive. If you still don't get it, ask someone who might know. But this is what I learned. So, don't think of them as signs, but as a pattern. 1 Negative = negative 2 Negative = positive 3 Negative = negative 4 Negative = positive And so on...


What is iit pattern for 2010?

The Indian Institute of Technology pattern has been same since 2004. It includes multiple choice questions and has negative marking too.