1. Exponents:
Exponents are used to convey huge numbers in a more readable, understandable, comparable, and manipulable format.
2. Expressing Large Numbers in the Standard Form:
- Any number between 1.01.0 and 10.010.0 (including 1.01.0) multiplied by a power of ten can be expressed as a decimal number between 1.01.0 and 10.010.0(including 1.01.0).
- The standard form of a number is also known as scientific motion.
3. Large numbers are difficult to read, comprehend, compare, and manipulate.
4. We use exponents to make all of this easier by transforming many of the enormous numbers into a shorter form.
5. What are some examples of exponential forms of numbers?
100=102100=102 (It can be read as 1010 raised to 22)
512=83512=83
243=35243=35
Here, 10, 810, 8 and 33 are the bases, whereas 2, 32, 3 and 55 are their respective exponents.
We also can say that
100100 is the 2nd2nd power of 1010 ,
512512 is the 3rd3rd power of 88 ,
243243 is the 5th5th power of 33 , etc.
6. For any non-zero integers aa and bb, and whole numbers mm and nn, numbers in exponential form obey the following laws:
a. am × an = am+nam × an = am+n
b. am ÷ an = am-n , m nam ÷ an = am-n , m n
c. (am)n = amn(am)n = amn
d. am × bm = (ab)mam × bm = (ab)m
e. am ÷ bm = (ab)mam ÷ bm = (ab)m
f. a0 = 1a0 = 1
g. (-1)(even number) = 1
h. (-1)(odd number) = -1Is this page helpful?
Prove that the following equation is correct 3−3×62×98−−√52×125−−−√3×(15)−43×313=282–√
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