Question

Show how to solve the equation in the picture

Answer 1

`\left(3\cdot8\cdot x\right)^7\\\\\left(3\cdot2\cdot4\cdot x\right)^7\\\\\left((3\cdot2)\cdot4\cdot x\right)^7\\\\\left(6\cdot4\cdot x\right)^7\\\\6^7\cdot4^7\cdot x^7\\\\`

In the second step, I rewrote 8 as 2*4. Then after that I regrouped terms so that the (3*2) can pair up together. This of course turns into 6. After that point, we have 6, 4 and x multiplied together as the base.

The last step uses the rule that
`(a*b*c)^d = a^d*b^d*c^d`, in other words, we apply the exponent d to each term inside the parenthesis. Each term inside gets its own exponent.

An example:
`(2*4*6)^3 = 2^3*4^3*6^3`