Express the following fraction in simplest form using only positive exponents.

Question

start fraction, 6, z, to the power 9 , divided by, 3, left parenthesis, z, right parenthesis, squared, end fraction
3(z)
2

6z
9

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Answer 1

To simplify the fraction \(\frac{6z^9}{3(z^2)}\), follow these steps:

1. Divide the coefficients: \[ \frac{6}{3} = 2 \]

2. Use the property of exponents: When you divide powers with the same base, you subtract the exponents: \[ z^{9-2} = z^{7} \]

3. Combine the results: Putting it all together, we have: \[ \frac{6z^9}{3(z^2)} = 2z^7 \]

Thus, the fraction in its simplest form using only positive exponents is: \[ \boxed{2z^7} \]