Question

If a, b, c are positive real numbers, then $\sqrt[5]{53125a^{10}{b}^5{c}^{10}}$ is equal to

• A. $5a^{2}b{c}^2$
• B. $25a{b}^{2}c$
• C. $5a^{3}bc$
• D. $125a^{2}b{c}^2$

Answer 1

The correct option is A

$5a^{2}b{c}^2$

$\sqrt[5]{53125a^{10}{b}^5{c}^{10}}=\sqrt[5]{55^5{a}^{10}{b}^5{c}^{10}}$

=${\left(5^5{a}^{10}{b}^5{c}^{10}\right)}^{\frac{1}{5}}=5^{5\times \frac{1}{5}}.a^{10\times \frac{1}{5}}.b^{5\times \frac{!}{5}}.c^{10\times \frac{1}{5}}=5a^{2}b{c}^2$