Answers:
1) [tex]x^{8} y^{8}[/tex]
2) [tex]y^{3} \sqrt{y}[/tex]
3) [tex]5x^{4} \sqrt{6}[/tex]
4) [tex]\sqrt{7}[/tex]
5) [tex]\frac{\sqrt{z}}{z}[/tex]
Step-by-step explanation:
1) [tex]\sqrt{x^{16} y^{36}}[/tex]
Rewriting the expression:
[tex](x^{16} y^{36})^{\frac{1}{2}}[/tex]
Multiplying the exponents:
[tex]x^{\frac{16}{2}} y^{\frac{36}{2}}[/tex]
Simplifying:
[tex]x^{8} y^{8}[/tex]
2) [tex]\sqrt{y^{7}}[/tex]
Rewriting the expression:
[tex]\sqrt{y^{6} y}=(y^{6} y)^{\frac{1}{2}}[/tex]
Multiplying the exponents:
[tex]y^{\frac{6}{2}} y^{\frac{1}{2}}[/tex]
Simplifying:
[tex]y^{3} y^{\frac{1}{2}}=y^{3} \sqrt{y}[/tex]
3) [tex]\sqrt{150 x^{8}}[/tex]
Rewriting the expression:
[tex]\sqrt{(6)(25) x^{8}}[/tex]
Since [tex]\sqrt{25}=5[/tex]:
[tex]5x^{4}\sqrt{6}[/tex]
4) [tex]\frac{7}{\sqrt{7}}[/tex]
Multiplying numerator and denominator by [tex]\sqrt{7}[/tex]:
[tex]\frac{7}{\sqrt{7}} (\frac{\sqrt{7}}{\sqrt{7}})=\frac{7}{7\sqrt{7}}[/tex]
Simplifying:
[tex]\sqrt{7}[/tex]
5) [tex]\frac{5z}{\sqrt{25 z^{3}}}[/tex]
Rewriting the expression:
[tex]\frac{5z}{5z \sqrt{z}}[/tex]
Simplifying:
[tex]\frac{1}{\sqrt{z}}[/tex]
Since we do not want the square root in the denominator, we can multiply numerator and denominator by [tex]\sqrt{z}[/tex]:
[tex]\frac{1}{\sqrt{z}}(\frac{\sqrt{z}}{\sqrt{z}})[/tex]
Finally:
[tex]\frac{\sqrt{z}}{z}[/tex]
