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Andreas93 [3]
2 years ago
11

Select the correct answer. Rewrite the following expression.

Mathematics
1 answer:
kolezko [41]2 years ago
7 0

The <em>algebraic</em> expression x^{10/3} is equivalent to the <em>algebraic</em> expression x^{3}\cdot \sqrt[3]{x}. Thus, the right choice is option D.

<h3>How to apply power and root properties to rewrite a given expression</h3>

In this question we must apply the following set of <em>algebraic</em> properties to simplify a given expression:

x^{m/n} = \sqrt[n]{x^{m}} = \left(\sqrt[n]{x}\right)^{m}   (1)

x^{m+n} = x^{m}\cdot x^{n}   (2)

x^{m\cdot n} = \left(x^{m}\right)^{n} = \left(x^{n}\right)^{m}   (3)

Where:

  • <em>m</em>, <em>n</em> - Exponents
  • <em>x</em> - Base

And also by apply the definition of power.

If we know that the given expression is x^{10/3}, then the equivalent expression is:

x^{10/3} = \sqrt[3]{x^{10}} = \sqrt[3]{x^{9}\cdot x} = \sqrt[3]{x^{9}}\cdot \sqrt[3]{x} = x^{3}\cdot \sqrt[3]{x}

The <em>algebraic</em> expression x^{10/3} is equivalent to the <em>algebraic</em> expression x^{3}\cdot \sqrt[3]{x}. Thus, the right choice is option D.

To learn more on roots, we kindly invite to check this verified question: brainly.com/question/1527773

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see explanation

Step-by-step explanation:

1

The cosine function in standard form is

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2

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Step-by-step explanation:

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