Archie Mead,

Thank you much for clarifying. Are these rules particular to these kinds of problems, with fractionized exponents? I was following the rule I saw in my textbook when I added the indices with that multiplication problem. The example is shown in my workbook as so:

\(\displaystyle

x^{5/6} * x^{2/3}

\)

\(\displaystyle

x^{9/6}

\)

However, I notice that they both use x and not different numbers like the example which I gave you. I would like for this to be as clear as possible for myself so that I won't have any trouble further down the road. :] Thank you very much for your help and your time.

Colton

Hi colton,

that one is slightly different....

\(\displaystyle x^{\frac{5}{6}}x^{\frac{2}{3}}=x^{\frac{5}{6}}x^{\frac{4}{6}}=x^{\frac{5}{6}+\frac{4}{6}}\)

In that case you add the exponents because x is a particular value.

You need to know the difference between when you add or multiply the exponents.

For example......

\(\displaystyle 2^22^3=(2*2)(2*2*2)\)

That's 5 twos multiplied together, so it's \(\displaystyle 2^5\)

However \(\displaystyle \left(2^2\right)^3=(2*2)(2*2)(2*2)\)

which is 6 twos multiplied together, so it's \(\displaystyle 2^6\)

\(\displaystyle x^a*x^b=x^{a+b}\)

\(\displaystyle \left(x^a\right)^b=x^{ab}\)

Also, as in your earlier example

\(\displaystyle x^a*y^a=(xy)^a\)

since \(\displaystyle 2^2*3^2=2*2*3*3=2*3*2*3=(2*3)(2*3)=(2*3)^2\) and so on