## Intermediate Algebra: Connecting Concepts through Application

$(10a^{3}bc^{9})^{\frac{1}{4}}=10^{\frac{1}{4}}a^{\frac{3}{4}}b^{\frac{1}{4}}c^{\frac{9}{4}}$
Step 1: The index of the radical is 4, so the denominator of the fractional exponent is 4. Step 2: Therefore, the expression is written as $(10a^{3}bc^{9})^{\frac{1}{4}}$. Step 3: $(10a^{3}bc^{9})^{\frac{1}{4}}=10^{\frac{1}{4}}a^{\frac{3}{4}}b^{\frac{1}{4}}c^{\frac{9}{4}}$