Answer:
Simplify the expression: [tex](16y^{\frac{5}{4}}y^3)^{\frac{1}{2}}[/tex]
Use the exponent power:
- [tex]a^n \cdot a^m = a^{n+m}[/tex]
- [tex]\sqrt[n]{a^n} =a[/tex]
- [tex](a^n)^m = a^{nm}[/tex]
[tex](16y^{\frac{5}{4}}y^3)^{\frac{1}{2}}[/tex]
Apply the given rules;
[tex](16y^{\frac{5}{4} +3} )^{\frac{1}{2}}[/tex]
Simplify:
[tex](16y^{\frac{17}{4}} )^{\frac{1}{2}}[/tex]
then;
[tex](16)^{\frac{1}{2}} \cdot (y^{\frac{17}{4}})^{\frac{1}{2}} = 4y^{\frac{17}{8}}[/tex]
Therefore, the simplified expression of [tex](16y^{\frac{5}{4}}y^3)^{\frac{1}{2}}[/tex] is, [tex]4y^{\frac{17}{8}}[/tex]
