How do you solve 64 diveded by 125 that number to the power of 2x-8 equals 25 diveded by 16 that number to the power of x Please show work?

Answer 1

(64/125)2x-8=(25/16)x

Ok, you first want to give them common bases:

(43/53)2x-8=(52/42)x

So because of the rule (xm)n=xmn, we can say:

(4/5)3(2x-8)=(5/4)2x

But you see that we still don't have the same bases, so in order to make them the same, we have to flip either one to make them equal. When you want to flip a fraction, you invert it by putting it to a power of -1.

(4/5)3(2x-8)=(4/5)-2x

Now, you can ignore the bases and set the exponents equal to each other.

3(2x-8)=-2x

And solve for x:

6x-24=-2x

-24=-8x

x=3