If {x^{xsqrt[3]{x}}} = {(x cdot sqrt[3]{x})^x | vedclass

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Question

(D) Given the equation: ${x^{x \cdot x^{1/3}}} = {(x \cdot x^{1/3})^x}$.Simplify the exponents: ${x^{x^{4/3}}} = {(x^{4/3})^x}$.This simplifies to: ${

Vedclass · Accepted Answer

$64/27$

Vedclass · Answer

(D) Given the equation: ${x^{x \cdot x^{1/3}}} = {(x \cdot x^{1/3})^x}$.Simplify the exponents: ${x^{x^{4/3}}} = {(x^{4/3})^x}$.This simplifies to: ${x^{x^{4/3}}} = {x^{(4/3)x}}$.For the bases to be equal,the exponents must be equal (assuming $x > 0$ and $x 
eq 1$):${x^{4/3}} = \frac{4}{3}x$.Divide by $x$ (since $x 
eq 0$):${x^{1/3}} = \frac{4}{3}$.Cube both sides:$x = (\frac{4}{3})^3 = \frac{64}{27}$.

If ${x^{x\sqrt[3]{x}}} = {(x \cdot \sqrt[3]{x})^x}$,then $x =$

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