Question: User: (16allover81)raise to the power 3all over 4
1. **State the problem:** Simplify the expression $$\left(\frac{16}{81}\right)^{\frac{3}{4}}$$.
2. **Recall the rule for fractional exponents:** $$a^{\frac{m}{n}} = \sqrt[n]{a^m} = \left(\sqrt[n]{a}\right)^m$$.
3. **Apply the rule:**
$$\left(\frac{16}{81}\right)^{\frac{3}{4}} = \left(\sqrt[4]{\frac{16}{81}}\right)^3$$.
4. **Calculate the fourth root of numerator and denominator separately:**
$$\sqrt[4]{16} = 2$$ because $$2^4 = 16$$.
$$\sqrt[4]{81} = 3$$ because $$3^4 = 81$$.
So,
$$\sqrt[4]{\frac{16}{81}} = \frac{2}{3}$$.
5. **Raise the result to the power 3:**
$$\left(\frac{2}{3}\right)^3 = \frac{2^3}{3^3} = \frac{8}{27}$$.
6. **Final answer:**
$$\left(\frac{16}{81}\right)^{\frac{3}{4}} = \frac{8}{27}$$.