Question

Express the following fraction in simplest form using only positive exponents.
start fraction, 6, z, to the power 9 , divided by, 3, left parenthesis, z, right parenthesis, squared, end fraction
3(z)
2

6z
9

​

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:
\[
\boxed{2z^7}
\]