Question

How do these two equations equal each other? I can't figure it out.

Answer 1

6^(7)4^(7)x^(7) = (23)^(7)(2^2)^(7)*x^(7) = 2^(7)*3^(7)*2^(14)*x^(7) = 3^(7)*2^(21)*x^(7)

3^(7)*2^(7)*2^(7)*x^(7) = 3^(7)*2^(21)*x^(7)

Cancelling out x^(7) from both sides

3^(7)*2^(7)*2^(7) = 3^(7)*2^(21)

Simplified

2^(7)*2^(7) = 2^(21) SLAY

Answer 2

These two equations are equal because they both simplify to:

(38x)^(7) = (3222x)^(7) = 3^(7)*2^(7)*2^(7)*x^(7)

and

6^(7)4^(7)x^(7) = (23)^(7)(2^2)^(7)*x^(7) = 2^(7)*3^(7)*2^(14)*x^(7) = 3^(7)*2^(21)*x^(7)

So, we have:

3^(7)*2^(7)*2^(7)*x^(7) = 3^(7)*2^(21)*x^(7)

Cancelling out x^(7) from both sides, we get:

3^(7)*2^(7)*2^(7) = 3^(7)*2^(21)

Simplifying, we get:

2^(7)*2^(7) = 2^(21)

which is true since 2^(7)2^(7) = (2222222)(2222222) = 2^(14), and 2^(21) = (2222222222222)(222222222222*2) = 2^(14)*2^(7).