Answer :
Let's simplify the radical expression [tex]\(\sqrt[4]{625 x^{12} y^8}\)[/tex].
1. Simplify the numerical part: [tex]\(\sqrt[4]{625}\)[/tex]
- Determine the 4th root of 625. Since [tex]\(5^4 = 625\)[/tex], we have:
[tex]\[
\sqrt[4]{625} = 5
\][/tex]
2. Simplify the variable part: [tex]\(\sqrt[4]{x^{12}}\)[/tex]
- Apply the property of exponents: [tex]\(\sqrt[4]{x^{12}} = x^{12/4} = x^3\)[/tex].
3. Simplify the variable part: [tex]\(\sqrt[4]{y^8}\)[/tex]
- Again, apply the property of exponents: [tex]\(\sqrt[4]{y^8} = y^{8/4} = y^2\)[/tex].
4. Combine the simplified parts:
- Put it all together to get the final expression:
[tex]\[
5 x^3 |y^2|
\][/tex]
Therefore, the simplified form of the expression [tex]\(\sqrt[4]{625 x^{12} y^8}\)[/tex] is [tex]\(5x^3|y^2|\)[/tex].
1. Simplify the numerical part: [tex]\(\sqrt[4]{625}\)[/tex]
- Determine the 4th root of 625. Since [tex]\(5^4 = 625\)[/tex], we have:
[tex]\[
\sqrt[4]{625} = 5
\][/tex]
2. Simplify the variable part: [tex]\(\sqrt[4]{x^{12}}\)[/tex]
- Apply the property of exponents: [tex]\(\sqrt[4]{x^{12}} = x^{12/4} = x^3\)[/tex].
3. Simplify the variable part: [tex]\(\sqrt[4]{y^8}\)[/tex]
- Again, apply the property of exponents: [tex]\(\sqrt[4]{y^8} = y^{8/4} = y^2\)[/tex].
4. Combine the simplified parts:
- Put it all together to get the final expression:
[tex]\[
5 x^3 |y^2|
\][/tex]
Therefore, the simplified form of the expression [tex]\(\sqrt[4]{625 x^{12} y^8}\)[/tex] is [tex]\(5x^3|y^2|\)[/tex].
