Di) 4. Which expression is equivalent to (a^3b^27c^9)^(1)/(3) Din) b^9c^3 4) ab^9c^3 d) b^81c^27 4) a^3b^81c^27

To simplify the expression \((a^{3}b^{27}c^{9})^{\frac{1}{3}}\), we apply the power of a power rule, which states that \((x^m)^n = x^{mn}\). <br /><br />So, we distribute the exponent \(\frac{1}{3}\) to each term inside the parentheses:<br /><br />\[<br />(a^{3}b^{27}c^{9})^{\frac{1}{3}} = a^{3 \cdot \frac{1}{3}} \cdot b^{27 \cdot \frac{1}{3}} \cdot c^{9 \cdot \frac{1}{3}}<br />\]<br /><br />This simplifies to:<br /><br />\[<br />a^{1} \cdot b^{9} \cdot c^{3} = ab^{9}c^{3}<br />\]<br /><br />Therefore, the expression equivalent to \((a^{3}b^{27}c^{9})^{\frac{1}{3}}\) is:<br /><br />(1) \(ab^{9}c^{3}\)