Question

If a, b, c are positive real numbers, then 5√3125a¹⁰b⁵c¹⁰ is equal to
A. 5a²bc²B. 25ab²cC. 5a³bc³D. 125a²bc²

Answer 1

The required "option B) $5a^{2}bc^{2}$" is correct.

Step-by-step explanation:

We have,

$\sqrt[5]{3125a^{10}b^{5}c^{10}}$

Where, a, b and c are positive real numbers

To find, the value of $\sqrt[5]{3125a^{10}b^{5}c^{10}}$ = ?

∴ $\sqrt[5]{3125a^{10}b^{5}c^{10}}$

= $(3125a^{10}b^{5}c^{10})^{\dfrac{1}{5} }$

Using the identity,

$\sqrt[n]{a} =a^{\dfrac{1}{n} }$

∵ 3125 = 5 × 5 × 5 × 5 × 5 = $5^{5}$

= $(5^5a^{10}b^{5}c^{10})^{\dfrac{1}{5} }$

= $5^{5\times \dfrac{1}{5}}a^{10\times \dfrac{1}{5}}b^{5\times \dfrac{1}{5}}c^{10\times \dfrac{1}{5}}$

= $5^{1}a^{2}b^{1}c^{2}$

= $5a^{2}bc^{2}$

∴ The value of $\sqrt[5]{3125a^{10}b^{5}c^{10}}$ = $5a^{2}bc^{2}$

Thus, the required "option B) $5a^{2}bc^{2}$" is correct.

Answer 2

it is the correct answer.. pls mark me as the brainliest