Question 36976
Think of exponents in the simplest way possible. Forget x, y, z, etc.
2 is a simple number (1 is really too simple for this)
{{{2*2*2*2 = 2^4}}}
count up the # of 2's - that's the exponent
{{{2*2*2*2*2*2*2 = 2^7}}}
now multiply
{{{2*2*2*2*2*2*2*2*2*2*2 = 2^11}}}
you just add the exponents
It's a lot easier to write {{{2^4 * 2^7 = 2^11}}} than all those 2's
That's the point of exponents- it's EASIER
but you have to acquire rules
like how do you add? {{{2^7 + 2^4}}}
not obvious
{{{2^7 + 2^4 = 2^4*(2^3 + 1)}}}
do it the long way, too
{{{2*2*2*2*2*2*2 + 2*2*2*2 = 2*2*2*2 * (2*2*2 + 1)}}}
I just factored out 2*2*2*2
go back and forth
easy way - hard way
easy way - hard way
If you play with it enough and show yourself what's true and 
what isn't- you'll have no trouble with the x's, y's, and z's
{{{5*x^4 - 12*x^3 = 0}}}
{{{x^3 * (5*x - 12) = 0}}}
I factored out x^3
what makes this true?
If x is zero, I get
0 times something = 0
that's certainly true
Inside the parenthesis, if x= 12/5, then
12/5*(12/5 - 12/5) = 0
that's certainly true, also
x = 0
x = 12/5
are the solutions