Chapter 10
209 Words
Chapter 10: Exponents and Powers
10.1 Introduction to Exponents
An exponent represents the number of times a number (called the base) is multiplied by itself. It is written as Ana^Nan, where aaa is the base and nnn is the exponent.
Example: 23=2×2×2=82^3 = 2 times 2 times 2 = 823=2×2×2=8
10.2 Laws of Exponents
Product of Powers: am×an=am+na’m times a^n = a^{m+n}am×an=am+n
Quotient of Powers: aman=am−nfrac{a PM}{a^n} = a^{m-n}anam=am−n
Power of a Power: (am)n=am×n(a PM)^n = a^{m times n}(am)n=am×n
Power of a Product: (ab)n=an×bn(ab)^n = a^n times b^n(ab)n=an×bn
Zero Exponent: a0=1a^0 = 1a0=1 (where a≠0a neq 0a=0)
Negative Exponent: a−n=1ana^{-n} = frac{1}{a^n}a−n=an1
Exercises
Exercise 1: Simplify the following expressions using the laws of exponents:
32×333^2 times 3^332×33
5452frac{5^4}{5^2}5254
(23)2(2^3)^2(23)2
(4×2)3(4 times 2)^3(4×2)3
7573frac{7^5}{7^3}7375
Exercise 2: Evaluate the following:
505^050
3−23^{-2}3−2
102×10310^2 times 10^3102×103
(22)3(2^2)^3(22)3
4341frac{4^3}{4^1}4143 Take your time solving these questions
Eslam Assem
Thank you
Maybe you will find it hard at the first time, but when you read the explanations carefully you will be able to solve it very well.
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