Question

Which expression is equivalent to (r^5/4

Answer 1

Answer:

2

Step-by-step explanation:

• Multiplying two numbers with same bases is the same as adding their powers:

∴ $(\frac{4^{\frac{5}{4} } \cdot 4^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }$

⇒ $(\frac{4^{\frac{5}{4} } ^ + ^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }$

⇒ $(\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }$

• Dividing two numbers with same bases is the same as subtracting their powers:

∴  $(\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }$

⇒ $(4^{{\frac{6}{4} - \frac{1}{2} }})^{\frac{1}{2} }$

⇒  $(4^{1})^{\frac{1}{2} }$

⇒  $4^{\frac{1}{2}$

• Raising anything to the power of  $\frac{1}{2}$ is the same as square-rooting it:

∴  $4^{\frac{1}{2}$

⇒ $\sqrt{4}$

⇒ 2