Simplifying rational expression with exponents

[Qwertyuiop[]]

Hi, i need to simplify and factor this expression , i get (-1/4)b^-35 . I used online calculators and they all get different answers LOL . I rewrote the expression in the usual format we are used to. The correct answer is -1/4 b^5 . I don't know how they get b^5 i got b^-35 . Symbolab calc gets a different answer and quickmaths calc gets this answer: b^95/ 65536. So what's the problem here ? What's the right way simplify these expressions ?

 

[topsquark]

The problem is order of operations. Your problem is actually
[imath]\dfrac{ \left ( \dfrac{ b^3 (2b^4) }{b^2} \right )^2 }{ \left ( \dfrac{ (-2b)^2 }{(-b)^6 } \cdot (-b)^5 \right )^5 }[/imath]

The difference is between [imath]a : b \cdot c = \dfrac{a}{b} \cdot c[/imath] and [imath]a : (b \cdot c) = \dfrac{a}{b \cdot c}[/imath].

-Dan

 

[Qwertyuiop[]]

The problem is order of operations. Your problem is actually
[imath]\dfrac{ \left ( \dfrac{ b^3 (2b^4) }{b^2} \right )^2 }{ \left ( \dfrac{ (-2b)^2 }{(-b)^6 } \cdot (-b)^5 \right )^5 }[/imath]

The difference is between [imath]a : b \cdot c = \dfrac{a}{b} \cdot c[/imath] and [imath]a : (b \cdot c) = \dfrac{a}{b \cdot c}[/imath].

-Dan

Thanks i got the right answer after rewriting it that way. So it has to do with BODMAS ? If no parentheses then a : b * c should be interpreted as (a/b) * c and not a/ (b*c). It becomes a / (b*c) only when there are parentheses right ?

 

[JeffM]

Thanks i got the right answer after rewriting it that way. So it has to do with BODMAS ? If no parentheses then a : b * c should be interpreted as (a/b) * c and not a/ (b*c). It becomes a / (b*c) only when there are parentheses right ?

Correct. With respect to multiplication and division, the order of operations proceeds left to right in pairs in the absence of grouping symbols, but grouping symbols take precedence over multiplication and division.

Let us suppose that

[math]a \div b = p, \ b * c = q, \ b \ne 0, \text { and } = c \ne 0.\\ \therefore \ a \div b \times c = p \times c, \text { but } a \div (b \times c) = a \div q.[/math]

 

[Deleted member 4993]

Symbolab calc gets a different answer and quickmaths calc gets this answer: b^95/ 65536

You have to be super-extra-careful during the input of these problems.

 

[Deleted member 4993]

Thanks i got the right answer after rewriting it that way. So it has to do with BODMAS ? If no parentheses then a : b * c should be interpreted as (a/b) * c and not a/ (b*c). It becomes a / (b*c) only when there are parentheses right ?

Correct....