Question

Solve the equation (3x2)(3x4)=36

Answer 1

Answer:

The solution to the equation will be:

$x=\sqrt[3]{2},\:x=-\sqrt[3]{2}$

or

$x = 1.26$ , $x = -1.26$

Step-by-step explanation:

Given the expression

$\left(3x^2\right)\left(3x^4\right)=36$

simplify

$9x^6=36$

Divide both sides by 9

$\frac{9x^6}{9}=\frac{36}{9}$

$x^6=4$

$\mathrm{For\:}x^n=f\left(a\right)\mathrm{,\:n\:is\:even,\:the\:solutions\:are\:}x=\sqrt[n]{f\left(a\right)},\:-\sqrt[n]{f\left(a\right)}$

$x=\sqrt[6]{4},\:x=-\sqrt[6]{4}$

solving

$x=\sqrt[6]{4}$

  $=\sqrt[6]{2^2}$

Apply exponent rule:   $\left(a^b\right)^c=a^{bc}$

  $=\sqrt[6]{2^2}=2^{2\cdot \frac{1}{6}}$

   $=\sqrt[3]{2}$

   $= 1.26$

Thus,

$x=\sqrt[3]{2}$   (or  $x = 1.26$ )

similarly solving

$x=-\sqrt[6]{4}$

$x=-\sqrt[3]{2}$  or ($x = -1.26$)

Therefore, the solution to the equation will be:

$x=\sqrt[3]{2},\:x=-\sqrt[3]{2}$

or

$x = 1.26$ , $x = -1.26$

Answer 2

Answer:

$3 {x}^{2} \times 3 {x}^{4} = 36 \\ 9 {x}^{6} = 36 \\ {x}^{6} = 4 \\ \boxed{x = \sqrt[6]{4} }$

is the right answer.