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Rewrite in simplest radical form [tex]\frac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}[/tex]. Show each step of your process.

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1. Start with the given expression: [tex]\frac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}[/tex].
2. Use the property of exponents: [tex]a^{m} / a^{n} = a^{m-n}[/tex].
3. Subtract the exponents: [tex]\frac{5}{6} - \frac{1}{6} = \frac{4}{6} = \frac{2}{3}[/tex].
4. The expression simplifies to: [tex]x^{\frac{2}{3}}[/tex].
5. Rewrite in radical form: [tex]\sqrt[3]{x^2}[/tex].

Thus, [tex]\frac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}[/tex] in simplest radical form is [tex]\sqrt[3]{x^2}[/tex].


Sagot :

Certainly! Let's simplify the given expression step by step.

We start with the fraction:

[tex]\[ \frac{x^{\frac{5}{6}}}{\frac{1}{6}} \][/tex]

When dividing by a fraction, we can multiply by its reciprocal. So, we rewrite the expression as:

[tex]\[ x^{\frac{5}{6}} \times \frac{6}{1} \][/tex]

Simplifying further, we multiply the exponents:

[tex]\[ x^{\frac{5}{6}} \times 6 = x^{\left(\frac{5}{6} \times 6\right)} \][/tex]

When we multiply the exponent [tex]\(\frac{5}{6}\)[/tex] by 6, we get:

[tex]\[ \frac{5}{6} \times 6 = 5 \][/tex]

So the expression simplifies to:

[tex]\[ x^{5} \][/tex]

Hence, the simplest radical form of [tex]\(\frac{x^{\frac{5}{6}}}{\frac{1}{6}}\)[/tex] is:

[tex]\[ x^5 \][/tex]

This means that after simplifying the original expression, we have [tex]\(x^5\)[/tex].