Question

Why is there not an absolute value for b?

Answer 1

one sec

Answer 2

\[\frac{\sqrt{a^2b^{10}}}{\sqrt{b}}\]

Answer 3

This is the problem I need to simplify and the answer is \[\left|a\right|b^4\sqrt{b}\]

Answer 4

Why does the b^4 not have an absolute value? My teacher in class told me the rule even exponents and even exponents with an odd exponent is an absolute value

Answer 5

b^4 cannot be negative and needs no absolute value symbol to indicate that it is.

a needs the absolute value symbol because it could be negative.

Answer 6

gotcha

Answer 7

b is undefined for b\(\ge\)0

Answer 8

\(\color{#000000 }{ \displaystyle \frac{ \sqrt{a^2b^{10}} }{\sqrt{~b~}} }\)

the absolute value \(z\) is defined as;
\(|z|=\sqrt{z^2~}\) (for real number \(z\))

\(\color{#000000 }{ \displaystyle \frac{ \sqrt{a^2b^{10}} }{\sqrt{~b~}} \Rightarrow \frac{ \sqrt{a^2}\cdot \sqrt{b^{10}} }{\sqrt{~b~}}\Rightarrow \frac{|a|\cdot \sqrt{\left(b^{5}\right)^2} }{\sqrt{~b~}}\Rightarrow\frac{ |a|\cdot |b^5| }{\sqrt{~b~}}}\)

then we will rationalize the denominator

\(\color{#000000 }{ \displaystyle \frac{ |a|\cdot |b^5|\cdot \sqrt{~b~} }{b} }\)

this is what I would be getting, but recalling that b is positive anyway,

\(\color{#000000 }{ \displaystyle \frac{ |a|\cdot b^5\cdot \sqrt{~b~} }{b} }\)

\(\color{#000000 }{ \displaystyle |a|\cdot b^4\cdot \sqrt{~b~} }\)