dymand68 said: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
dymand68 said: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
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.dymand68 said:the total given example:
(3.5709*10^5)+(5.789*10^4)
=(35.709*10^4)+(5.789*10^4)
dymand68 said:=(35.709 + 5.789)(10^4 + 10^4)
=41.498 * 10^4
=4.1498*10^5
The "Addition of exponents disconnect" is a mathematical concept where adding two exponents with the same base does not result in the expected sum.
This occurs because the rules of exponents state that when multiplying two exponential terms with the same base, the exponents should be added. However, when adding two exponential terms with the same base, the exponents cannot be added and must be multiplied instead.
Sure, let's look at the expression 2^3 + 2^4. According to the rule, the exponents should be added resulting in 2^7. However, when we expand the expression, we get 8 + 16 = 24, which is not equal to 2^7.
Yes, it is a common mistake made by students when first learning about exponents. It is important to understand the rules of exponents and when they can and cannot be applied.
To avoid making mistakes, always remember the rules of exponents and be careful when adding exponential terms with the same base. It is also helpful to practice and review problems using exponents to reinforce your understanding.