0 is not defined.^{0}
Negative integer exponents:0 is not defined for any positive n^{-n}
n root of ^{th}x for integer n > 1 , also written as and is defined as: 1. For odd integers n > 1, the nth root is a unique real number which when raised to the power of n, gives x 2. For even integers n>1 : a. If n, gives xb. If 0c. If x for even integer n is not a real number (it is a complex number)
(x if ^{1/n})^{m}x is a real number^{1/n}Laws of exponents and radicals:
The number In scientific notation any number is represented as a is decimal and is called significand or mantissa (which means “meaningful” part), and b is an integer exponent. When the absolute value of a is between 1 and 10, as in the above examples, the representation is called normalized scientific notation.
The scientific notation represents the “meaningful” part of the number in an easily readable form as a decimal number with absolute value between
- Determine the significand / mantissa:
Find the “meaningful” part (non-zero digits) and write it placing the decimal point after the first digit: in our example this will give you 4.3 (the significand or mantissa). Preserve the positivity or negativity of the original value – positive decimal number will result in a positive mantissa and negative decimal number will result in negative mantissa. Placing the point after the first digit ensures that the mantissa absolute value is between - Determine the exponent:
Count how many positions you have to move the decimal point between the scientific notation (significand) decimal point position and the decimal number representation point position. In this example we have to move the decimal point 11 positions to the left, as the original value is “small”. When moving to the left (representing a ”small” number) the exponent will be negative (because we are dividing by -11
- Then our original number
*0.000 000 000 043*written in scientific notation is*4.3 x 10*^{-11}.
This operation is more straightforward – we only have to move the decimal point of the mantissa the number of positions indicated by the exponent (left for negative exponent / “small” number and right for positive exponent / “large” number).
the mantissa / “meaningful” part will be 2) Convert 0.000 27 |