easy exponents

[deagez]

what is a quick way to think about the following?

2^5+2^5+3^5+3^5+3^5

[truplayer256]

2^5+2^5+3^5+3^5+3^5

2*(2^5)+3*(3^5)=2^(5+1)+3^(5+1)=2^6+3^6

[mehravikas]

Shouldn't it be - 2^6+3^7

2^5+2^5+3^5+3^5+3^5

2*(2^5)+3*(3^5)=2^(5+1)+3^(5+1)=2^6+3^6

[tohellandback]

Shouldn't it be - 2^6+3^7

2^5+2^5+3^5+3^5+3^5

2*(2^5)+3*(3^5)=2^(5+1)+3^(5+1)=2^6+3^6

no. coz 3*3^5=3^(5+1)=3^6

[struggling_guy2001]

Hi,


Wanna to remind you the very basic formula or property behind this...

(a) ^ (x) * (a) ^ (y) = (a) ^ (x+y).

[mehravikas]

In the question 3^5 appears thrice: 3^5+3^5+3^5

Shouldn't it be - 2^6+3^7

2^5+2^5+3^5+3^5+3^5

2*(2^5)+3*(3^5)=2^(5+1)+3^(5+1)=2^6+3^6

no. coz 3*3^5=3^(5+1)=3^6

[tohellandback]

In the question 3^5 appears thrice: 3^5+3^5+3^5

Shouldn't it be - 2^6+3^7

2^5+2^5+3^5+3^5+3^5

2*(2^5)+3*(3^5)=2^(5+1)+3^(5+1)=2^6+3^6

no. coz 3*3^5=3^(5+1)=3^6

yes and thats why it is 3 * 3^5. Now 3* 3^5=3^6

[mehravikas]

Are you trying to say the occurrence of an integer does not matter?

2^5+2^5 = 2^6

3^5+3^5+3^5 = 3^6

In the question 3^5 appears thrice: 3^5+3^5+3^5

Shouldn't it be - 2^6+3^7

2^5+2^5+3^5+3^5+3^5

2*(2^5)+3*(3^5)=2^(5+1)+3^(5+1)=2^6+3^6

no. coz 3*3^5=3^(5+1)=3^6

yes and thats why it is 3 * 3^5. Now 3* 3^5=3^6

[tohellandback]

Are you trying to say the occurrence of an integer does not matter?

2^5+2^5 = 2^6

3^5+3^5+3^5 = 3^6

In the question 3^5 appears thrice: 3^5+3^5+3^5

Shouldn't it be - 2^6+3^7

2^5+2^5+3^5+3^5+3^5

2*(2^5)+3*(3^5)=2^(5+1)+3^(5+1)=2^6+3^6

no. coz 3*3^5=3^(5+1)=3^6

yes and thats why it is 3 * 3^5. Now 3* 3^5=3^6

Ummm I am trying to say that its a formula for exponents which can be explained in multiple ways. And I suggest you take any book even the OG and go through the exponents basics once. Should not take more than 20 minutes.

[mehravikas]

Thanks..Basically I got confused in a step that was not explained in the answer explanations:

3^5+3^5+3^5 = 3^5(1 + 1 + 1) = 3^5 * 3^1 = 3^6

Cheers,
Vikas

Are you trying to say the occurrence of an integer does not matter?

2^5+2^5 = 2^6

3^5+3^5+3^5 = 3^6

In the question 3^5 appears thrice: 3^5+3^5+3^5

Shouldn't it be - 2^6+3^7

2^5+2^5+3^5+3^5+3^5

2*(2^5)+3*(3^5)=2^(5+1)+3^(5+1)=2^6+3^6

no. coz 3*3^5=3^(5+1)=3^6

yes and thats why it is 3 * 3^5. Now 3* 3^5=3^6

Ummm I am trying to say that its a formula for exponents which can be explained in multiple ways. And I suggest you take any book even the OG and go through the exponents basics once. Should not take more than 20 minutes.

[Ian Stewart]

Thanks..Basically I got confused in a step that was not explained in the answer explanations:

3^5+3^5+3^5 = 3^5(1 + 1 + 1) = 3^5 * 3^1 = 3^6

Nothing wrong with factoring here, as you did above, to see that 3^5 + 3^5 + 3^5 = 3^6. You can also notice that we're simply adding the same thing three times, which is what it means to multiply by 3:

x + x + x = 3x

so 3^5 + 3^5 + 3^5 = 3*(3^5)