Question

a friend is having trouble with exponents and ask you to review some worked problems look over the problems and correct any mistakes find the correct any mistakes find the correct answer and explain the error in the student reasoning

Answer 1

Given the following expression:

`\text{ }(4a^2b^5)/(2a^6b^2)`

To be able to simplify this type of expression, let's first separate like terms before doing the operation:

We get,

`\text{ }(4a^2b^5)/(2a^6b^2)\text{ = }(4)/(2)\text{ x }(a^2)/(a^6)\text{ x }(b^5)/(b^2)`

In dividing like terms, we simply copy the base and subtract the exponent of the term on the numerator by the exponent of the like term on the denominator.

`\text{ }(a^x)/(a^y)=a^(x-y)`

We get,

`(4)/(2)\text{ x }(a^2)/(a^6)\text{ x }(b^5)/(b^2)=2a^(2-6)b^(5-2)`
`2a^(2-6)b^(5-2)=2a^(-4)b^3`

For a case of a negative exponent, reciprocate that term.

`a^(-4)\text{ = }(1)/(a^4)`

We get,

`\text{ 2a}^(-4)b^3\text{ = }(2b^3)/(a^4)`

Therefore, the answer is:

`(2b^3)/(a^4)`

The error in the student's solution is that on the part of subtracting the exponent of the a variable, 2-6 = -4 not 4, the student forgot the rule of subtracting numbers by larger ones.