Question

(25 pts!!! help needed asap) x2y3z Write the expression in exponential form. A) x2yz4 B) x6y7z4 C) x 1 2 y 3 4 z D) x 1 2 y 3 4 z 1 4

Answer 1

D

Explanation:

Given expression :

• 
  `\sqrt[4]{x^(2)y^(3)z }`

Solving :

• A number with the 4th root is the same as a number raised to the power 1/4
• 
  `(x^(2))^(1/4)(y^(3))^(1/4)(z)^(1/4)`
• 
  `x^{(1)/(2)} y^{(3)/(4)}z^{(1)/(4) }` [Option D]

Answer 2

D
`\sf x^(\frac12) y^(\frac34) z^(\frac14)`

Explanation:

`\sqrt[4]{\sf x^2y^3z}=\sqrt[4]{\sf x^2y^3z^1}`

Apply the Radical Product Rule
`√(\sf ab) =√(\sf a)√(\sf b)` :

`\implies \sqrt[4]{\sf x^2}\sqrt[4]{\sf y^3}\sqrt[4]{\sf z}`

Apply fractional exponent rule
`\sqrt[n]{\sf a^m} = \sf a^{(m)/(n)}` :

`\sf \implies x^(\frac24) y^(\frac34) z^(\frac14)`

Simplify:

`\sf \implies x^(\frac12) y^(\frac34) z^(\frac14)`