Answer:
[tex]\sqrt[7]{x^{4}}[/tex]
[tex](x^{\frac{1}{7}})^{4}[/tex]
[tex](\sqrt[7]{x})^{4}[/tex]
Step-by-step explanation:
we have
[tex]x^{\frac{4}{7}}[/tex]
Remember the properties
[tex]\sqrt[n]{a^{m}}=a^{\frac{m}{n}}[/tex]
[tex](a^m)^{n}=a^{m*n}[/tex]
so
Verify each case
Part 1) we have
[tex]\sqrt[4]{x^{7}}[/tex]
we know that
[tex]\sqrt[4]{x^{7}}=x^{\frac{7}{4}}[/tex]
Compare with the given expression
[tex]x^{\frac{7}{4}} \neq x^{\frac{4}{7}}[/tex]
Part 2) we have
[tex]\sqrt[7]{x^{4}}[/tex]
we know that
[tex]\sqrt[7]{x^{4}}=x^{\frac{4}{7}}[/tex]
Compare with the given expression
[tex]x^{\frac{4}{7}} = x^{\frac{4}{7}}[/tex]
therefore
Is equivalent to the given expression
Part 3) we have
[tex](x^{\frac{1}{7}})^{4}[/tex]
we know that
[tex](x^{\frac{1}{7}})^{4}=x^{\frac{4}{7}}[/tex]
Compare with the given expression
[tex]x^{\frac{4}{7}} = x^{\frac{4}{7}}[/tex]
therefore
Is equivalent to the given expression
Part 4) we have
[tex](x^{\frac{1}{4}})^{7}[/tex]
we know that
[tex](x^{\frac{1}{4}})^{7}=x^{\frac{7}{4}}[/tex]
Compare with the given expression
[tex]x^{\frac{7}{4}} \neq x^{\frac{4}{7}}[/tex]
Part 5) we have
[tex](\sqrt[4]{x})^{7}[/tex]
we know that
[tex](\sqrt[4]{x})^{7}=(x^{\frac{1}{4}})^{7}=x^{\frac{7}{4}}[/tex]
Compare with the given expression
[tex]x^{\frac{7}{4}} \neq x^{\frac{4}{7}}[/tex]
Part 6) we have
[tex](\sqrt[7]{x})^{4}[/tex]
we know that
[tex](\sqrt[7]{x})^{4}=(x^{\frac{1}{7}})^{4}=x^{\frac{4}{7}}[/tex]
Compare with the given expression
[tex]x^{\frac{4}{7}} = x^{\frac{4}{7}}[/tex]
therefore
Is equivalent to the given expression
