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Simplify the radical expression:

[tex]\sqrt[4]{625 x^{12} y^8}[/tex]

A. [tex]5 x^3\left|y^2\right|[/tex]

B. [tex]25 x^9\left|y^4\right|[/tex]

C. [tex]51 x^3 y^2[/tex]

D. [tex]25\left|x^9\right| y^4[/tex]

Answer :

To simplify the radical expression [tex]\(\sqrt[4]{625 x^{12} y^8}\)[/tex], let's break it down step-by-step:

1. Simplify the Constant 625:
- Find the fourth root of 625. Since [tex]\(5^4 = 625\)[/tex], the fourth root of 625 is 5.

2. Simplify the Variable [tex]\(x^{12}\)[/tex]:
- For [tex]\(x^{12}\)[/tex], you take the fourth root by dividing the exponent by 4:
[tex]\[
x^{12/4} = x^3
\][/tex]

3. Simplify the Variable [tex]\(y^8\)[/tex]:
- For [tex]\(y^8\)[/tex], take the fourth root by dividing the exponent by 4:
[tex]\[
y^{8/4} = y^2
\][/tex]

4. Combine the Results:
- Putting it all together, the simplified form of the radical expression is:
[tex]\[
5 x^3 |y^2|
\][/tex]

This shows that [tex]\(\sqrt[4]{625 x^{12} y^8}\)[/tex] simplifies to [tex]\(5 x^3 |y^2|\)[/tex].

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