1. **Stating the problem:** We want to find the value of $$\frac{8^{\frac{3}{5}} \times 94^{5}}{81^{\frac{1}{8}} \times 64^{\frac{1}{5}}}$$. 2. **Recall the properties of exponents:** - $$a^{m} \times a^{n} = a^{m+n}$$ - $$\left(a^{m}\right)^{n} = a^{m \times n}$$ - $$\frac{a^{m}}{a^{n}} = a^{m-n}$$ - $$\left(\frac{a}{b}\right)^{n} = \frac{a^{n}}{b^{n}}$$ 3. **Simplify each term:** - $$8^{\frac{3}{5}}$$: Since $$8 = 2^{3}$$, then $$8^{\frac{3}{5}} = \left(2^{3}\right)^{\frac{3}{5}} = 2^{3 \times \frac{3}{5}} = 2^{\frac{9}{5}}$$. - $$94^{5}$$ remains as is (94 is prime factorization not simple, so keep it). - $$81^{\frac{1}{8}}$$: Since $$81 = 3^{4}$$, then $$81^{\frac{1}{8}} = \left(3^{4}\right)^{\frac{1}{8}} = 3^{\frac{4}{8}} = 3^{\frac{1}{2}}$$. - $$64^{\frac{1}{5}}$$: Since $$64 = 2^{6}$$, then $$64^{\frac{1}{5}} = \left(2^{6}\right)^{\frac{1}{5}} = 2^{\frac{6}{5}}$$. 4. **Rewrite the expression:** $$\frac{2^{\frac{9}{5}} \times 94^{5}}{3^{\frac{1}{2}} \times 2^{\frac{6}{5}}}$$ 5. **Combine powers of 2:** $$\frac{2^{\frac{9}{5}}}{2^{\frac{6}{5}}} = 2^{\frac{9}{5} - \frac{6}{5}} = 2^{\frac{3}{5}}$$ 6. **Final simplified expression:** $$2^{\frac{3}{5}} \times \frac{94^{5}}{3^{\frac{1}{2}}}$$ 7. **Interpretation:** This is the simplified form. Without further factorization or decimal approximation, this is the exact simplified result. **Final answer:** $$2^{\frac{3}{5}} \times \frac{94^{5}}{3^{\frac{1}{2}}}$$