What is index form ?
When a number is expressed with exponents, or one number to a power of another, it is considered to be in index form.
To write the the given product of prime factors in index form, we will follow the steps given below.
Step 1 :
Observe the terms and count it how many times they are repeated.
Step 2 :
The term which is repeated should be written in the base and the number of times repeated should be in the power.
Note :
If we see the term once, the power should be considered as 1.
Write each number in index form :
Problem 1 :
2×2×3×3x3
Solution :
= 2×2×3×3×3
Here, 2 is repeated 2 times and 3 is repeated 3 times.
So the exponential form is 2^{2} × 3^{3}.
Problem 2 :
2×5×5
Solution :
= 2×5×5
Here, 2 is repeated once and 5 is repeated 2 times.
So the exponential form is 2^{1} × 5^{2}.
Problem 3 :
2×3×3×3×5
Solution :
= 2×3×3×3×5
Here 2 and 5 are repeated once and 3 is repeated 3 times.
So the exponential form is 2^{1} × 3^{3 }× 5^{1}.
Problem 4 :
5×5×7×7
Solution :
= 5×5×7×7
5 is repeated 2 times and 7 is repeated 2 times.
So the exponential form is 5^{2} × 7^{2}.
Problem 5 :
2 × 2 × 5 × 5 × 5 × 7
Solution :
= 2 × 2 × 5 × 5 × 5 × 7
2 is repeated 2 times, and 5 is repeated 3 times and 7 is repeated once.
So the exponential form is 2^{2} × 5^{3} × 7^{1}.
Problem 6 :
3×3×7×7×11×11
Solution :
= 3×3×7×7×11×11
Here 3, 7 and 11 is repeated 2 times.
So the exponential form is 3^{2} × 7^{2} × 11^{2}.
Problem 7 :
2×2×2×3×3×3×3
Solution :
= 2×2×2×3×3×3×3
2 is repeated 3 times, and 3 is repeated 4 times.
So the exponential form is 2^{3} × 3^{4}.
Problem 8 :
5×5×5×5×5×5×7×7×7
Solution :
= 5×5×5×5×5×5×7×7×7
5 is repeated 6 times, and 7 is repeated 3 times.
So the exponential form is 5^{6} × 7^{3}.
Write the following in exponent form :
Problem 1 :
25
Solution :
= 25
= 5×5
Here 5 is repeated 2 times.
So, the exponential form is 5^{2}.
Problem 2 :
36
Solution :
= 36
= 6×6
6 is repeated 2 times.
So, the exponential form is 6^{2}.
Problem 3 :
125
Solution :
125 = 5×5×5 5 is repeated 3 times. So, the exponential form is 5^{3}. |
Problem 4 :
343
Solution :
343 = 7 × 7 × 7 Here, 7 is repeated 3 times
So, the exponential form is 7^{3}. |
Write the following in exponent form with 3 as a base :
Problem 1 :
3
Solution :
Since, 3 is in the base, we don’t have any power for 3,
So, consider 3^{1}.
So the exponential form is 3^{1}.
Problem 2 :
27
Solution :
27 = 3 × 3 × 3 Since, 3 is repeated 3 times So the exponential form is 3^{3}. |
Problem 3 :
81
Solution :
= 3 × 3 × 3 × 3 = 3^{4} Since, 3 is repeated 4 times So the exponential form is 3^{4}. |
Problem 4 :
729
Solution :
= 3 × 3 × 3 × 3 × 3 × 3 = 3^{6} Here, 3 is repeated 6 times So the exponential form is 3^{6}. |
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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