Question

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

Answer 1

`3 {x}^(2) * 3 {x}^(4) = 36 \\ 9 {x}^(6) = 36 \\ {x}^(6) = 4 \\ \boxed{x = \sqrt[6]{4} }`

is the right answer.

Answer 2

The solution to the equation will be:

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

or

`x = 1.26` ,
`x = -1.26`

Explanation:

Given the expression

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

simplify

`9x^6=36`

Divide both sides by 9

`(9x^6)/(9)=(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 (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`