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NNADVOKAT [17]
2 years ago
12

Rewrite the expression with rational exponents as a radical expression.

Mathematics
1 answer:
Alik [6]2 years ago
3 0

Answer:

\displaystyle 4\sqrt[7]{x^3}

General Formulas and Concepts:

<u>Algebra I</u>

  • Exponential Rule [Root Rewrite]:                                                                        \displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

<em />\displaystyle 4x^\bigg{\frac{3}{7}}<em />

<em />

<u>Step 2: Rewrite</u>

  1. Split:                                                                                                                      \displaystyle 4(x^\bigg{\frac{1}{7}})^3
  2. Rewrite [Exponential Rule - Root Rewrite]:                                                        \displaystyle 4\sqrt[7]{x^3}
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Answer:

\large \begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:c & \sf Sum\:of\:Factors\\\cline{1-2} 1, -22 & -21 \\\cline{1-2} -1, 22 & 21\\\cline{1-2} 2, -11 & -9 \\\cline{1-2} -2, 11 & 9 \\\cline{1-2}\end{array}

Step-by-step explanation:

Quadratic equation: ax² + bx + c = 0, where a ≠ 0

x² + 9x - 22

  • a = 1
  • b = 9
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Factors of c (-22):

1 × -22     or     -1 × 22

2 × -11      or     -2 × 11

Sum of factors:

1 + (-22) = -21          or          -1 + 22 = 21

2 + (-11) = -9            or           -2 + 11 = 9

Table:

\large \begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:c & \sf Sum\:of\:Factors\\\cline{1-2} 1, -22 & -21 \\\cline{1-2} -1, 22 & 21\\\cline{1-2} 2, -11 & -9 \\\cline{1-2} -2, 11 & 9 \\\cline{1-2}\end{array}

Hope this helps!

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Step-by-step explanation:

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