Answer:
2
Step-by-step explanation:
• Multiplying two numbers with same bases is the same as adding their powers:
∴ [tex](\frac{4^{\frac{5}{4} } \cdot 4^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](\frac{4^{\frac{5}{4} } ^ + ^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
• Dividing two numbers with same bases is the same as subtracting their powers:
∴ [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](4^{{\frac{6}{4} - \frac{1}{2} }})^{\frac{1}{2} }[/tex]
⇒ [tex](4^{1})^{\frac{1}{2} }[/tex]
⇒ [tex]4^{\frac{1}{2}[/tex]
• Raising anything to the power of [tex]\frac{1}{2}[/tex] is the same as square-rooting it:
∴ [tex]4^{\frac{1}{2}[/tex]
⇒ [tex]\sqrt{4}[/tex]
⇒ 2
