which expression is equivalent to $sqrt3{125x^{6}y^{15}z^{3}}$?\n$5x^{3}y^{3}z$\n$5x^{2}y^{5}z$\n$25x^{2}y^{3…

Explanation:

Step1: Simplify the cube - root of 125

The cube - root of 125 is 5 since (5\times5\times5 = 125), i.e., (\sqrt[3]{125}=5).

Step2: Simplify the cube - root of (x^{6})

Using the rule (\sqrt[n]{a^{m}}=a^{\frac{m}{n}}), for (n = 3) and (m = 6), we have (\sqrt[3]{x^{6}}=x^{\frac{6}{3}}=x^{2}).

Step3: Simplify the cube - root of (y^{15})

Using the rule (\sqrt[n]{a^{m}}=a^{\frac{m}{n}}), for (n = 3) and (m = 15), we get (\sqrt[3]{y^{15}}=y^{\frac{15}{3}}=y^{5}).

Step4: Simplify the cube - root of (z^{3})

The cube - root of (z^{3}) is (z) since (\sqrt[3]{z^{3}}=z^{\frac{3}{3}}=z).

Step5: Combine the simplified terms

(\sqrt[3]{125x^{6}y^{15}z^{3}}=\sqrt[3]{125}\cdot\sqrt[3]{x^{6}}\cdot\sqrt[3]{y^{15}}\cdot\sqrt[3]{z^{3}} = 5x^{2}y^{5}z).

Answer:

B. (5x^{2}y^{5}z)