Question

Express the following fraction in simplest form, only using positive exponents.
start fraction, 3, y, to the power 6 , divided by, 4, left parenthesis, y, to the power minus 1 , right parenthesis, cubed, end fraction
4(y
−1
)
3

3y
6

​

Answer 1

To simplify the given fraction \(\frac{3y^6}{4(y^{-1})^3}\), we can follow these steps:

1. **Simplify the denominator**:
\[
(y^{-1})^3 = y^{-3}
\]
So the denominator becomes:
\[
4y^{-3}
\]

2. **Rewrite the fraction**:
Now, we have:
\[
\frac{3y^6}{4y^{-3}}
\]

3. **Use the property of exponents**:
We know that dividing by \(y^{-3}\) is the same as multiplying by \(y^3\):
\[
\frac{3y^6}{4y^{-3}} = \frac{3y^6 \cdot y^3}{4}
\]
Combine the exponents of \(y\):
\[
y^6 \cdot y^3 = y^{6 + 3} = y^9
\]

4. **Combine everything**:
Now the expression becomes:
\[
\frac{3y^9}{4}
\]

5. **Express in simplest form**:
The fraction \(\frac{3y^9}{4}\) is already in simplest form, using only positive exponents.

Thus, the final answer is:
\[
\frac{3y^9}{4}
\]