How do you simplify sqrt(z^3)sqrt(z^7)?

1 Answer
David B.
Jul 12, 2016

We use the properties of powers to find sqrt(z^3) * sqrt(z^7) = z^5

Explanation:

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 1/2, i.e.:

sqrt(z^3) * sqrt(z^7) = (z^3)^(1/2) * (z^7)^(1/2)

Now we use the property that raising a power to another power multiplies the exponents:

(z^3)^(1/2) * (z^7)^(1/2) = z^(3/2) * z^(7/2)

Then we use the property that multiplying powers with the same base adds the exponents:

z^(3/2) * z^(7/2) = z^(3/2+7/2) = z^(10/2) = z^5

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