exponents and power chapter notes please,i promise to mark brainest if you answer correctly
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Step-by-step explanation:
Exponents
We can write large numbers in a short form using exponents.
For example: 10,000 = 10 × 10 × 10 × 10 = 104
Here, ‘10’ is called the base and ‘4’ the exponent. The number 104 is read as 10 raised to the power of 4 or simply as the fourth power of 10.
104 is called the exponential form of 10,000.
(1)any natural number = 1
(-1)an odd natural number = -1
(-1)an even natural number = +1
am × an = am+n, where m and n are whole numbers and a (≠ 0) is an integer.
This formula can be used to write answers to above questions.
For any non-zero integer a,
am ÷ an = am-n where m and n are whole numbers and m > n.
For any non-zero integer a,
(am)n = amn (where m and n are whole numbers)
For any non-zero integer a
am × bm = (ab)m (where m is any whole number)
Expressing Large Numbers in the Standard Form
Large numbers can be expressed conveniently using exponents. Such a number is said to be in standard form if it can be expressed as k × 10m, where 1 ≤, k < 10 and m is a natural number.
Note that, one less than the digit count (number of digits) to the left of the decimal point in a given number, is the exponent of 10 in the standard form.
For any rational number a and positive integer n, we define an as a × a × a × …… × a (n times). an is known as the nth power of a and is read as ‘a raised to the power n’. The rational a is called the base and n is called the exponent or power.
e.g. 10,000 = 10 × 10 × 10 × 10 = 104.
10 is the base and 4 is the exponent.
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