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].
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].
