ab²- which part is squared.

[Wendy1]

if a=5, b=3
ab²
I thought this should be 5x3=15² so then 15x15=225
but apparently it's 5x3² I don't understand - I thought that as ab means axb that would mean that the result from axb would be then the part that is squared??

 

[MarkFL]

As written:

[MATH]ab^2=a\cdot b^2[/MATH]
If it were written as:

[MATH](ab)^2[/MATH]
then that is equivalent to:

[MATH]a^2b^2[/MATH]

 

[Wendy1]

Thank you.

 

[Dr.Peterson]

if a=5, b=3
ab²
I thought this should be 5x3=15² so then 15x15=225
but apparently it's 5x3² I don't understand - I thought that as ab means axb that would mean that the result from axb would be then the part that is squared??

What you did would be right if we evaluated an expression left to right: 5, then multiply by 3, then square the result.

The standard "order of operations" in algebra is different. Exponents are applied first, then multiplications. So in an expression like yours, [MATH]ab^2[/MATH], the exponent 2 applies only to the single entity next to it, the [MATH]b[/MATH]; after applying that, then we multiply [MATH]a[/MATH] times [MATH]b^2[/MATH].