Question: el 3) showing fraction in simplest form, only using pos
$$\frac{10h^{10}}{(-5h^{5}q)^{3}}$$
1. **State the problem:** Simplify the expression $$\frac{10h^{10}}{(-5h^{5}q)^{3}}$$ to its simplest form using only positive exponents.
2. **Apply the exponent to the denominator:** Use the power of a product rule $$ (abc)^n = a^n b^n c^n $$ to expand the denominator:
$$(-5)^{3} (h^{5})^{3} (q)^{3} = -125 h^{15} q^{3}$$
3. **Rewrite the fraction:**
$$\frac{10h^{10}}{-125 h^{15} q^{3}}$$
4. **Simplify the coefficients:**
$$\frac{10}{-125} = \frac{\cancel{10}^{1}}{\cancel{125}^{12.5}} = -\frac{2}{25}$$
5. **Simplify the variables:**
For $$h$$, subtract exponents in numerator and denominator:
$$h^{10} / h^{15} = h^{10-15} = h^{-5}$$
Since we want positive exponents, rewrite:
$$h^{-5} = \frac{1}{h^{5}}$$
6. **Combine all parts:**
$$-\frac{2}{25} \times \frac{1}{h^{5} q^{3}} = -\frac{2}{25 h^{5} q^{3}}$$
**Final answer:**
$$\boxed{-\frac{2}{25 h^{5} q^{3}}}$$