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What is zero exponent?
If a number (other than 0) has 0 as an exponent, it equals 1! It may be hard to believe but it is true, no matter what number. If a number has no exponent, there is basically an invisible 1 as the exponent, so the number would be equal to itself. Zero with the exponent zero is meaningless.
What is an irrational exponent?
It means that it is an exponent, and that it is not a rational number - i.e., one that can be written as a fraction of two integers.
In Algebra what is exponent?
One way to view the exponent, especially when it is a natural number, is how many times something need to be multiplied by itself. So 4^5 has exponent 5 and base 4 and it means 4 multiplied by itself 5 times, ie 4x4x4x4x4 We can then extent this to negative integers and to an exponent of zero and then to rational exponents. More on that if you want to know.
What are the rules in changing scientific notation to standard notation and standard notation to scientific notation?
To convert a number to scientific notation, move the decimal point right or left to make the number greater than or equal to one but less than ten, and record the number of positions moved as a power of 10 - the exponent. That is, if the decimal point moves to the left by n positions, then the exponent is 10n. If the decimal point moved to the right by npositions, the exponent is 10-n (note the minus symbol).For instance, the number 123,456,000,000 is larger than 10, so we move the decimal point 11 positions to the left to get 1.23456, which is greater than or equal to one, but less than ten. Since we moved the decimal point to the left by 11 positions, the exponent is 1011 (ten raised to the eleventh power, which is 100,000,000,000) so the scientific notation for 123,456,000,000 becomes 1.23456x1011.If the original number were 0.000000123456, we need to move the decimal point to the right by seven positions to get 1.23456 (greater than or equal to one but less than ten). The exponent is therefore 10-7, thus the scientific notation for 0.000000123456 is 1.23456x10-7.To convert from scientific notation to standard notation, we simply reverse the process. If the exponent is a positive power of 10, we multiply by the exponent. Thus 1.23456x1011 is 1.23456 x 100,000,000,000 which is 123,456,000,00. If the exponent is a negative power of 10, we divide by the exponent. Thus 1.23456x10-7 is 1.23456 / 10,000,000 which is 0.000000123456.Note that scientific notation is only useful when you are not interested in the least significant portion of a number. For instance, a value such as 123,456,789,123,456,789,123,456,789 is better notated in full if you want the highest degree of accuracy. Scientific notation is generally only used to make the notation of an extremely large (or extremely small) number more concise. So 123,456,789,123,456,789,123,456,789 might be reduced to a more concise form such as 1.23456789x1026. This then equates to 123,456,790,000,000,000,000,000,000 in standard notation, which is clearly not the same value we started out with. In other words, the degree of accuracy is determined by the number of decimal places you retain in the scientific notation.
What is 0.1 as a negative exponent?
Anything to the power of a negative number is equal to one divided that "anything" raised to the positive value of the exponent. For example:a-b = 1/ abSo you can think of this by expressing the number as a fraction. Consider, what is 0.1 as a fraction? The answer is 1/10. This means that when expressed as an exponent, it would be 10-1.
