Write the following expression in simplified radical form

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Mar 11,2025

Question

Write the following expression in simplified radical form $$ \sqrt[4]{96 x^{13} z^{4}} $$

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ \sqrt[4]{96x^{13}z^{4}} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\sqrt[4]{96x^{13}z^{4}}$$
- step1: Write as a product:
  $$\sqrt[4]{16	imes 6x^{13}z^{4}}$$
- step2: Write in exponential form:
  $$\sqrt[4]{2^{4}	imes 6x^{13}z^{4}}$$
- step3: Rewrite the exponent:
  $$\sqrt[4]{2^{4}	imes 6x^{12+1}z^{4}}$$
- step4: Expand the expression:
  $$\sqrt[4]{2^{4}	imes 6x^{12}	imes xz^{4}}$$
- step5: Reorder the terms:
  $$\sqrt[4]{2^{4}x^{12}z^{4}	imes 6x}$$
- step6: Use the properties of radicals:
  $$\sqrt[4]{2^{4}x^{12}z^{4}}	imes \sqrt[4]{6x}$$
- step7: Simplify the root:
  $$2zx^{3}\sqrt[4]{6x}$$
The expression $$ \sqrt[4]{96x^{13}z^{4}} $$ can be simplified to $$ 2zx^{3}\sqrt[4]{6x} $$ in simplified radical form.
The simplified radical form of $$ \sqrt[4]{96x^{13}z^{4}} $$ is $$ 2zx^{3}\sqrt[4]{6x} $$.

Write the following expression in simplified radical form

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