Question

Which expression is equivalent to (r^5/4

Answer 1

2

Explanation:

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

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

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

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

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

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

⇒
`(4^{{(6)/(4) - (1)/(2) }})^{(1)/(2) }`

⇒
`(4^(1))^{(1)/(2) }`

⇒
`4^{(1)/(2)`

• Raising anything to the power of
`(1)/(2)` is the same as square-rooting it:

∴
`4^{(1)/(2)`

⇒
`√(4)`

⇒ 2