Question

The expression \[b^{-3\2} , b>0 \] is the equivalent to?

Answer 1

`a^(m)/(n)=\sqrt[n]{a^m}\\\\a^(-n)=(1)/(a^n)\\----------\\\\b^{-(3)/(2)}=\left((1)/(b)\right)^(3)/(2)=\left((1)/(b)\right)^{1(1)/(2)}=\left((1)/(b)\right)^{1+(1)/(2)}=(1)/(b)\cdot\left((1)/(b)\right)^(1)/(2)=(1)/(b)\cdot(1)/(b^(1)/(2))\\\\=(1)/(b)\cdot(1)/(√(b))=(1)/(b√(b))=(1\cdot√(b))/(b√(b)\cdot√(b))=(√(b))/(b\cdot b)=(√(b))/(b^2)`


`Answer:\boxed{b^{-(3)/(2)}=(√(b))/(b^2)}`

Answer 2

The expression \[b^{-3\2} , b>0 \] is the equivalent to;

=1/b3/2=1/b3−−√