Answer:
The solution to the equation will be:
[tex]x=\sqrt[3]{2},\:x=-\sqrt[3]{2}[/tex]
or
[tex]x = 1.26[/tex] , [tex]x = -1.26[/tex]
Step-by-step explanation:
Given the expression
[tex]\left(3x^2\right)\left(3x^4\right)=36[/tex]
simplify
[tex]9x^6=36[/tex]
Divide both sides by 9
[tex]\frac{9x^6}{9}=\frac{36}{9}[/tex]
[tex]x^6=4[/tex]
[tex]\mathrm{For\:}x^n=f\left(a\right)\mathrm{,\:n\:is\:even,\:the\:solutions\:are\:}x=\sqrt[n]{f\left(a\right)},\:-\sqrt[n]{f\left(a\right)}[/tex]
[tex]x=\sqrt[6]{4},\:x=-\sqrt[6]{4}[/tex]
solving
[tex]x=\sqrt[6]{4}[/tex]
[tex]=\sqrt[6]{2^2}[/tex]
Apply exponent rule: [tex]\left(a^b\right)^c=a^{bc}[/tex]
[tex]=\sqrt[6]{2^2}=2^{2\cdot \frac{1}{6}}[/tex]
[tex]=\sqrt[3]{2}[/tex]
[tex]= 1.26[/tex]
Thus,
[tex]x=\sqrt[3]{2}[/tex] (or [tex]x = 1.26[/tex] )
similarly solving
[tex]x=-\sqrt[6]{4}[/tex]
[tex]x=-\sqrt[3]{2}[/tex] or ([tex]x = -1.26[/tex])
Therefore, the solution to the equation will be:
[tex]x=\sqrt[3]{2},\:x=-\sqrt[3]{2}[/tex]
or
[tex]x = 1.26[/tex] , [tex]x = -1.26[/tex]
