Addition of exponents disconnect

[dymand68]

Homework Statement

(35.709 + 5.789)(10^4 + 10^4)
=41.498 * 10^4

Homework Equations

this is an an example given in my TEAS (standardized skills test) work book/study guide...is it accurate? i don't know why (10^4 + 10^4) = 10^4 after the simplification

The Attempt at a Solution

 

[berkeman]

Homework Statement

(35.709 + 5.789)(10^4 + 10^4)
=41.498 * 10^4

Homework Equations

this is an an example given in my TEAS (standardized skills test) work book/study guide...is it accurate? i don't know why (10^4 + 10^4) = 10^4 after the simplification

The Attempt at a Solution

That is not standard scientific (exponential) notation. Are you sure it wasn't written like this?

(35.709*10^4 + 5.789*10^4)

That would be more standard. Written as you show it, it is indeed wrong, or at least confusing.

 

[dymand68]

the total given example:
(3.5709*10^5)+(5.789*10^4)
=(35.709*10^4)+(5.789*10^4)
=(35.709 + 5.789)(10^4 + 10^4)
=41.498 * 10^4
=4.1498*10^5

 

[berkeman]

the total given example:
(3.5709*10^5)+(5.789*10^4)
=(35.709*10^4)+(5.789*10^4)
=(35.709 + 5.789)(10^4 + 10^4)
=41.498 * 10^4
=4.1498*10^5

Weird. I've certainly never seen that notation, and IMO it shouldn't be used. If the 3rd line were:

=(35.709 + 5.789)(10^4)

then I would be okay with that. But not the way they wrote it.

 

[Mark44]

the total given example:
(3.5709*10^5)+(5.789*10^4)
=(35.709*10^4)+(5.789*10^4)

The step below is wrong. Both terms above have a factor of 10^4, so the next line should be = (35.709 + 5.789) * 10^4.

It should be noted that 10^4 + 10^4 = 2*10^4, and this should further convince you that the next line is wrong.

=(35.709 + 5.789)(10^4 + 10^4)
=41.498 * 10^4
=4.1498*10^5

Whoever worked the example got the correct answer, but two steps along the way are incorrect.

 

[dymand68]

thank you, fwiw-the source is
ATI, Assessment Technologies Institute, LLC
Test of Essential Academic Skills Pre-Test Study Manual, edition 3.0