Answer:
11. [tex]57^{6/8}[/tex]
12. [tex]Y^{14/2}[/tex]
13. [tex]m^{\frac{o+p}{n}}[/tex]
14. [tex]81^{\frac{3}{50+x}}[/tex]
15. [tex]5^{2/3}[/tex]
Step-by-step explanation:
When converting from radicals to rational exponents, there's a quick, easy rule to remember:
- [tex]\sqrt[n]{x} =\sqrt[\text{index}]{\text{radicand}}[/tex]
- the exponent is [tex]\frac{\text{power}}{\text{root}}[/tex]
- [tex]\sqrt[n]{x} = x^{1/n}[/tex]
The "power" represents the exponent of the radical/radicand, while the "root" represents the index.
11. the eight root of fifty-seven to the sixth degree.
- Write the expression in radical form: [tex]\sqrt[8]{57^6}[/tex]
- Rewrite using the exponent rule (power over root): [tex]57^{6/8}[/tex]
12. the square root of Y to the fourteenth power.
- Write the expression in radical form: [tex]\sqrt[2]{Y^{14}}[/tex]
- Rewrite using the exponent rule (power over root): [tex]Y^{14/2}[/tex]
13. the nth root of m to the o plus p degree.
- Write the expression in radical form: [tex]\sqrt[n]{m^{o+p}}[/tex]
- Rewrite using the exponent rule (power over root): [tex]m^{\frac{o+p}{n}}[/tex]
14. The fifth root plus x of eighty-one to the third power.
- Write the expression in radical form: [tex]\sqrt[5+x]{81^{3}}[/tex]
- Rewrite using the exponent rule (power over root): [tex]81^{\frac{3}{50+x}}[/tex]
15. The cube root of five squared.
- Write the expression in radical form: [tex]\sqrt[3]{5^{2}}[/tex]
- Rewrite using the exponent rule (power over root): [tex]5^{2/3}[/tex]
