Question

Express the following fraction in simplest form, only using positive exponents.
start fraction, 15, w, to the power 6 , divided by, minus, 3, left parenthesis, w, to the power 4 , right parenthesis, to the power 4 , end fraction
−3(w
4
)
4

15w
6

​

Answer 1

To simplify the fraction \(\frac{15w^6}{-3(w^4)^4}\), we can follow these steps:

1. **Simplify the denominator**:
\[
(w^4)^4 = w^{4 \times 4} = w^{16}
\]
So, the denominator becomes:
\[
-3w^{16}
\]

2. **Rewrite the fraction**:
\[
\frac{15w^6}{-3w^{16}}
\]

3. **Simplify the coefficients**:
\[
\frac{15}{-3} = -5
\]

4. **Simplify the variable part using the properties of exponents**:
\[
\frac{w^6}{w^{16}} = w^{6 - 16} = w^{-10}
\]

5. **Combine the results**:
\[
-5w^{-10}
\]

To express this using only positive exponents, we can rewrite \(w^{-10}\) as \(\frac{1}{w^{10}}\). Therefore, we have:
\[
-5w^{-10} = -\frac{5}{w^{10}}
\]

So, the fraction in simplest form is:
\[
-\frac{5}{w^{10}}
\]