How do you undo exponents when different exponents are on each side of the equation?

Answer 1

I'm assuming that you're asking how to solve equations like this "x2 = y3", right? If you solve for x in equations such as this, you should keep in mind that y will probably have a fractional power or will be the radicand in a radical whose index isn't 2 (in other words, it won't be in a square root). You should also be conscious of the rule for converting radicals to exponents: xa/b equals the b-root of x to the a power.

So, to solve x2 = y3 for x, take the square root of both sides. This results in (x2)1/2 = (y3)1/2. You know that raising a quantity to a power when addition and substraction are absent means that you have to multiply the exponents, so you would then obtain x = y3/2. Using the conversion rule, x equals the square root of y cubed. It is a square root because the denominator of the exponent of y (or "b" if you're looking at the conversion rule) is 2, but things will not always work out so nicely. I hope this helped.