Question

hallar el exponente final de x
ayudaaaa porfavor ​

Answer 1

Respuesta:

10

Explicación paso a paso:

*se sabe:

xᵃ/xᵇ =xᵃ⁻ᵇ

xᵃxᵇ=xᵃ⁺ᵇ

(xᵃ)ᵇ= xᵃᵇ

$\sqrt[a]{x^{b} } =x^{b/a}$

*resolviendo:

$T=(\frac{\frac{\sqrt[4]{x}}{\sqrt[6]{x}}+\sqrt[12]{x}}{\frac{2\sqrt[3]{x}\sqrt[9]{x}}{\sqrt{x}}} )^{72}$

$T=(\frac{\frac{x^{1/4}}{x^{1/6}}+x^{1/12}}{\frac{2x^{1/3}x^{1/9}}{x^{1/2}}})^{72}$

$T=(\frac{x^{(1/4)-(1/6)}+x^{1/12}}{\frac{2x^{(1/3)+(1/9)}}{x^{1/2}}})^{72}$

$T=(\frac{x^{1/12}+x^{1/12}}{\frac{2x^{4/9} }{x^{1/2}}})^{72}$

$T=(\frac{2x^{1/12} }{2x^{(4/9)-(1/2)} } )^{72}$

$T=(\frac{x^{1/12} }{x^{-1/18} } )^{72}$

$T=(x^{(1/12)+(1/18)} )^{72}$

$T=(x^{5/36)} )^{72}$

$T=x^{5(72)/36}$

$T=x^{5(2)}$

$T=x^{10}$