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(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

(25 pts!!! help needed asap) x2y3z Write the expression in exponential form. A) x-example-1
User Pradhan
by
2.7k points

2 Answers

23 votes
23 votes

Answer:

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]
User Sebastian Hoitz
by
2.4k points
16 votes
16 votes

Answer:

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)

User Sumama Waheed
by
2.4k points