How do you simplify #sqrt(z^3)sqrt(z^7)#?
We use the properties of powers to find
We need to write the powers of the factors in a single number so that we can add them. We start by noting that a square root is just a power of
Now we use the property that raising a power to another power multiplies the exponents:
Then we use the property that multiplying powers with the same base adds the exponents: