Which is equivalent

Question

asked Dec 22, 2020 159k views

2 Answers

Bindiya Patoliya · Answer 1 · 2020-12-23T07:53:51+0000

Answer: Second option

$(x^5y)^{(1)/(3)} = x^{(5)/(3)}y^{(1)/(3)}$

Explanation:

By definition we know that:

$a ^{(m)/(n)} = \sqrt[n]{a^m}$

In this case we have the following expression

$\sqrt[3]{x^5y}$

Using the property mentioned above we can write an equivalent expression for
$\sqrt[3]{x^5y}$

$\sqrt[3]{x^5y} = (x^5y)^{(1)/(3)}$

$(x^5y)^{(1)/(3)} = x^{(5)/(3)}y^{(1)/(3)}$

Therefore the correct option is the second option

Omar · Answer 2 · 2020-12-28T11:47:28+0000

Answer:

x^(5)/(3) y^(1)/(3)

Explanation:

This question is on rules of rational exponential

where the exponential is a fraction, you can re-write it using radicals where the denominator of the fraction becomes the index of the radical;

General expression

$a^(1)/(n) =\sqrt[n]{a}$

Thus
$\sqrt[3]{x} =x^(1)/(3)$

Applying the same in the question

$\sqrt[3]{x^5y} =x^(5)/(3) y^(1)/(3)$

=
x^(5)/(3) y^(1)/(3)