a. Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 + 3 ^5 ?
1. 5^6
2. 13^5
3.2^6 + 3^6
4. 2^7 + 3^8
5. 4^5 + 9^5
Ans : 2^6 + 3^6
b. The value of 10^8 - 10^2 /10^7- 10^3, is the closed to which of the following ?
1. 1
2. 10
3. 10^2
4. 10^3
5. 10^4
Ans : 10
Please help to solve this problem ?
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b. The value of 10^8 - 10^2 /10^7- 10^3, is the closed to which of the following ?
1. 1
2. 10
3. 10^2
4. 10^3
5. 10^4
Ans : 10[/quote]
sOLUTION:
10^8 - 10^2/10^7- 10^3
= 10^2 (10^6-1)/ 10^3(10^4 - 1)
= 10^6-1 / 10 (10^4-1)
nOW 10^6-1 IS APPROX EQUAL TO 10^6 AND 10^4-1 IS APPROX EQUAL TO 10^4
hENCE
= 10^6/ (10 *10^4)
= 10^6/10^5
=10 WHICH IS THE ANSWER!
1. 1
2. 10
3. 10^2
4. 10^3
5. 10^4
Ans : 10[/quote]
sOLUTION:
10^8 - 10^2/10^7- 10^3
= 10^2 (10^6-1)/ 10^3(10^4 - 1)
= 10^6-1 / 10 (10^4-1)
nOW 10^6-1 IS APPROX EQUAL TO 10^6 AND 10^4-1 IS APPROX EQUAL TO 10^4
hENCE
= 10^6/ (10 *10^4)
= 10^6/10^5
=10 WHICH IS THE ANSWER!
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I am sorry but I don't understand how we can get the answer 2^6 + 3^6 for question 1 in the thread. Can someone please explain??
Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 + 3 ^5 ?
1. 5^6
2. 13^5
3.2^6 + 3^6
4. 2^7 + 3^8
5. 4^5 + 9^5
Ans : 2^6 + 3^6
Many Thanks
Which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 + 3 ^5 ?
1. 5^6
2. 13^5
3.2^6 + 3^6
4. 2^7 + 3^8
5. 4^5 + 9^5
Ans : 2^6 + 3^6
Many Thanks
- DanaJ
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I think you will agree with me that 2^5 + 2^5 + 3^5 + 3^5 + 3 ^5 is two times 2^5 plus three times 3^5. Now let's write that down:
2*2^5 + 3*3^5 = (2^1)*(2^5) + (3^1)(3^5). When multiplying powers of the same number, just add the exponents! So you get that 2^5 + 2^5 + 3^5 + 3^5 + 3 ^5 = 2^6 + 3^6.
2*2^5 + 3*3^5 = (2^1)*(2^5) + (3^1)(3^5). When multiplying powers of the same number, just add the exponents! So you get that 2^5 + 2^5 + 3^5 + 3^5 + 3 ^5 = 2^6 + 3^6.
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sOLUTION:shuklat wrote:b. The value of 10^8 - 10^2 /10^7- 10^3, is the closed to which of the following ?
1. 1
2. 10
3. 10^2
4. 10^3
5. 10^4
Ans : 10
10^8 - 10^2/10^7- 10^3
= 10^2 (10^6-1)/ 10^3(10^4 - 1)
= 10^6-1 / 10 (10^4-1)
nOW 10^6-1 IS APPROX EQUAL TO 10^6 AND 10^4-1 IS APPROX EQUAL TO 10^4
hENCE
= 10^6/ (10 *10^4)
= 10^6/10^5
=10 WHICH IS THE ANSWER![/quote]
Can you please explain this step by step I still find it very confusing