Write the following in simplified radical form.

Assume that the variable represents a positive real number.

Question

Write the following in simplified radical form. $$ \sqrt[5]{96 v^{14}} $$ Assume that the variable represents a positive real number.

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ \sqrt[5]{96v^{14}} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\sqrt[5]{96v^{14}}$$
- step1: Write as a product:
  $$\sqrt[5]{32	imes 3v^{14}}$$
- step2: Write in exponential form:
  $$\sqrt[5]{2^{5}	imes 3v^{14}}$$
- step3: Rewrite the exponent:
  $$\sqrt[5]{2^{5}	imes 3v^{10+4}}$$
- step4: Expand the expression:
  $$\sqrt[5]{2^{5}	imes 3v^{10}	imes v^{4}}$$
- step5: Reorder the terms:
  $$\sqrt[5]{2^{5}v^{10}	imes 3v^{4}}$$
- step6: Use the properties of radicals:
  $$\sqrt[5]{2^{5}v^{10}}	imes \sqrt[5]{3v^{4}}$$
- step7: Simplify the root:
  $$2v^{2}\sqrt[5]{3v^{4}}$$
The simplified radical form of $$ \sqrt[5]{96v^{14}} $$ is $$ 2v^{2}\sqrt[5]{3v^{4}} $$.
The simplified radical form is $$ 2v^{2}\sqrt[5]{3v^{4}} $$.

Write the following in simplified radical form.

Assume that the variable represents a positive real number.

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Write the following in simplified radical form. Assume that the variable represents a positive real number.

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Solución

Beyond the Answer

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Write the following in simplified radical form.

Assume that the variable represents a positive real number.