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

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Question

(A) Given the equation: ${x^{x \cdot x^{1/3}}} = {(x \cdot x^{1/3})^x}$Simplify the exponents: ${x^{x^{1 + 1/3}}} = {(x^{1 + 1/3})^x}$${x^{x^{4/3}}} =

Vedclass · Accepted Answer

$64/27$

Vedclass · Answer

(A) Given the equation: ${x^{x \cdot x^{1/3}}} = {(x \cdot x^{1/3})^x}$Simplify the exponents: ${x^{x^{1 + 1/3}}} = {(x^{1 + 1/3})^x}$${x^{x^{4/3}}} = {(x^{4/3})^x}$${x^{x^{4/3}}} = {x^{(4/3)x}}$Equating the exponents: ${x^{4/3}} = \frac{4}{3}x$Divide both sides by $x$ (assuming $x 
eq 0$): ${x^{4/3 - 1}} = \frac{4}{3}$${x^{1/3}} = \frac{4}{3}$$x = (\frac{4}{3})^3 = \frac{64}{27}$Note: $x=1$ is also a solution since $1^1 = 1^1$.

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

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