Example 5Įxpress the following numbers as a product of powers of prime factors:
Similarly, a 2 b 3 and b 3 a 2 are the same. Thus, a 3 b 2 = a 3 × b 2 = b 2 × a 3 = b 2 a 3. On the other hand, a 3 b 2 and b 2 a 3 are the same, since the powers of a and b in these two terms are the same. Note that in the case of terms a 3 b 2 and a 2 b 3 the powers of a and b are different. Since 9 > 8, so, 3 2 is greater than 2 3 Example 3 Which one is greater 2 3 or 3 2 ? Solution Instead of taking a fixed number let us take any integer a as the base, and write the numbers as,Ī × a = a 2 (read as ‘a squared’ or ‘a raised to the power 2’)Ī × a × a = a 3 (read as ‘a cubed’ or ‘a raised to the power 3’)Ī × a × a × a = a 4 (read as a raised to the power 4 or the 4 th power of a)Ī × a × a × a × a × a × a = a 7 (read as a raised to the power 7 or the 7 th power of a) and so on.Ī × a × a × b × b can be expressed as a 3b 2 (read as a cubed b squared)Ī × a × b × b × b × b can be expressed as a 2b 4 (read as a squared into b raised to the power of 4). You can also extend this way of writing when the base is a negative integer. Also identify the base and the exponent in each case.
In 2 5, 2 is the base and 5 is the exponent.įind five more such examples, where a number is expressed in exponential form. Similarly, 2 5 = 2 × 2 × 2 × 2 × 2 = 32, which is the fifth power of 2. What is the exponent and the base in 5 3? So, we can say 125 is the third power of 5. For example,ġ0 2, which is 10 raised to the power 2, also read as ‘10 squared’ andġ0 3, which is 10 raised to the power 3, also read as ‘10 cubed’.ĥ 3 means 5 is to be multiplied by itself three times, i.e., 5 3 = 5 × 5 × 5 = 125 For example:Ĩ1 = 3 × 3 × 3 × 3 can be written as 81 = 3 4, here 3 is the base and 4 is the exponent. However the base can be any other number also. In all the above given examples, we have seen numbers whose base is 10. Try writing these numbers in the same way 172, 5642, 6374. We have used numbers like 10, 100, 1000 etc., while writing numbers in an expanded form. In both these examples, the base is 10 in case of 103, the exponent is 3 and in case of 10 5 the exponent is 5. Here again, 10 3 is the exponential form of 1,000. Since 1,000 is 10 multiplied by itself three times, We can similarly express 1,000 as a power of 10. 10 4 is called the exponential form of 10,000. The number 10 4 is read as 10 raised to the power of 4 or simply as fourth power of 10. Here ‘10’ is called the base and ‘4’ the exponent. The short notation 104 stands for the product 10×10×10×10. We can write large numbers in a shorter form using exponents.
Exponential form how to#
In this Chapter, we shall learn about exponents and also learn how to use them. To make these numbers easy to read, understand and compare, we use exponents. These very large numbers are difficult to read, understand and compare. Can you read these numbers? Which distance is less? Do you know what the mass of earth is? It is
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